section6_logistic_regression.jl

### A Pluto.jl notebook ###
# v0.19.46

using Markdown
using InteractiveUtils

# ╔═╡ 661b028c-260c-41f8-9d8a-13cfea4c7e22
using Turing

# ╔═╡ bce03358-19c9-11ed-31d9-5b0929af50b6
begin
    using PlutoUI
	using StatsPlots
	using Plots; default(fontfamily="Computer Modern", framestyle=:box) # LaTex-style
    # using Turing
	using DataFrames
	using StatsFuns: logistic
    using Random
	using LaTeXStrings
	using Logging; Logging.disable_logging(Logging.Warn);
end;

# ╔═╡ 74a2053f-ef53-41df-8afc-997c166e6f67
begin
	using RDatasets
	# Import the "Default" dataset.
	default_df = dataset("ISLR", "Default");
	# Show the first six rows of the dataset.
	first(default_df, 6)
end

# ╔═╡ 920b9b1f-b56d-465c-bce2-e08530ec4bb4
using StatsBase

# ╔═╡ 0a8fff98-24fd-49d6-a6b2-061e6350350b
TableOfContents()

# ╔═╡ ccc43bd4-2149-4136-87f4-a4d251fc1f7a
md"[**↩ Home**](https://lf28.github.io/BayesianModelling/) 


[**↪ Next Chapter**](./section7_glm.html)
"

# ╔═╡ 9810605e-586b-4f38-a43c-4240cb91e154
md"""
# Bayesian logistic regression 
"""

# ╔═╡ e752d05f-bc3c-42a4-ac5a-0517637c59b9
md"""

## Frequentist's logistic regression

### The model
Recall linear regression's probabilistic model:

```math
p(y_n|\mathbf{x}_n, \beta_0, \boldsymbol{\beta}_1, \sigma^2) = \mathcal{N}(y_n; \mu(\mathbf{x}_n), \sigma^2),
```
where ``\mu`` is a linear function of the input ``\mathbf{x}_n``
```math
\mu(\mathbf{x}_n) = \beta_0+\mathbf{x}_n^\top \boldsymbol{\beta}_1,
```
and a Gaussian likelihood is assumed for the target ``y_n``. 

For binary classifications, ``y_n`` can only take binary choices (assume ``y_n\in \{0,1\}``). To reflect the change, a Bernoulli likelihood seems more suitable. However, a direct replacement of the mean parameter such as 

```math
\text{WRONG: }\;\;p(y_n|\mathbf{x}_n, \beta_0, \boldsymbol{\beta}_1) = \texttt{Bernoulli}(y_n; \mu(\mathbf{x}_n))= \begin{cases} \mu(\mathbf{x}_n) & y_n=1\\ 1-\mu(\mathbf{x}_n) & y_n=0\end{cases}
```

would not work, since a Bernoulli distribution's parameter needs to be between 0 and 1 but ``\mu(\mathbf{x})\in \mathbb{R}`` as a linear function is not constrained.


A remedy is to impose a ``\mathbb{R}\rightarrow [0,1]`` function to squeeze an unconstrained input of ``\mu`` to be between 0 and 1. And the logistic function does exactly the trick. The function is defined as

```math
\texttt{logistic}(\mu) \triangleq \sigma(\mu) = \frac{1}{1+e^{-\mu}}.
``` 

We use ``\sigma`` as a shorthand notation for the logistic transformation. The function is plotted below:

$(begin
plot(logistic, xlabel=L"\mu", ylabel="", label=L"\texttt{logistic}(\mu)", legend=:topleft, lw=2, size=(450,300))
end)

Note that no matter what the input is, the output is always between 0 and 1, which is exactly what we need.

"""

# ╔═╡ 793a70b2-af69-4b4c-b4c0-8eef3b4654e9
md"""

To put the above steps together, we have the frequentist's probabilistic model for logistic regression:


!!! information "Logistic regression"
	```math
	p(y_n|\mathbf{x}_n, \boldsymbol{\beta}) = \texttt{Bernoulli}(y_n; \sigma(\mu_n)),
	```
	where ``\mu_n= \beta_0 + \mathbf{x}_n^\top\boldsymbol{\beta}_1``.
"""

# ╔═╡ af482903-2975-48d7-a4fe-4cebfa337a2b
md"""

### Estimation

A logistic regression model can be fit again by maximising the likelihood function

```math
\hat{\boldsymbol{\beta}} \leftarrow \arg\max  p(\mathbf{y}|\mathbf{X}, \boldsymbol{\beta}).
```

Since the optimization problem has no closed-form analytical solution, an iterative gradient-based optimisation algorithm such as gradient descent is usually used to find the MLE estimator. In Julia, logistic regressions can be fit by using `GLM.jl`.
"""

# ╔═╡ ada4ad28-358e-4144-9d5c-f3b1d27deff1
md"""
### A toy example

"""

# ╔═╡ 7a189076-f53f-48ed-ace2-ffbcc287ff6f
begin
	D1 = [
	    7 4;
	    5 6;
	    8 6;
	    9.5 5;
	    9 7
	]
	
	D2 = [
	    2 3;
	    3 2;
	    3 6;
	    5.5 4.5;
	    5 3;
	]

	D = [D1; D2]
	targets = [ones(5); zeros(5)]
	AB = [1.5 8; 10 1.9]
end;

# ╔═╡ 1068259e-a7f6-4a56-b526-59e080c54d27
begin
	using GLM
	glm_fit = glm([ones(size(D)[1]) D], targets, Bernoulli(), LogitLink())
end

# ╔═╡ 60a5cad4-c676-4334-8cbe-47877a68943f
md"""
We have plotted the fit model below. It can be observed the fitted regression function, defined as 

```math
p(y_n=1|\mathbf{x}_n, \hat\beta_0, \hat{\boldsymbol{\beta}}_1) = \hat{\sigma}(\mu_n)= \frac{1}{1+\exp(- \hat\beta_0 - \mathbf{x}_n^\top\hat{\boldsymbol{\beta}}_1)}
```

is a very sharp S-shaped surface valued between 0 and 1. Towards the top right corner of the input space, the prediction is closer to 1.0, entailing the output ``y_n`` is more likely to be positive (or class 1). And the model also implies a linear decision boundary as expected.
"""

# ╔═╡ ccda7f54-67ee-4d17-a16c-6f8597447d1e
md"""
#### Pathological frequentist's prediction
One thing worth noting is the sharpness of the prediction surface. Data points on one side of the thin decision boundary are all indistinguishably predicted with either ``p(y_n=1|\ldots)=1,`` or ``0``. Such a clean-cut prediction is counter-intuitive. It should be naturally expected that 
* predictions near the boundary should be more uncertain than those further away 
* predictions further away from the observed data (marked as ```A, B``` in the figure) should be more uncertain.

We will see next how Bayesian approaches the problem and provides us with an alternative prediction which is more reasonable.
"""

# ╔═╡ e2918ef9-7f86-4d3b-93cb-65b8b5f48987
md"""

## Bayesian logistic regression


The Bayesian model reuses the likelihood function for ``\mathbf{y}``, but also imposes a prior on the regression parameter ``\beta_0, \boldsymbol{\beta}_1``. The final model is very similar to the linear regression equivalent, where we assume Gaussian priors for the regression parameter ``\beta_0, \boldsymbol{\beta}_1``.

!!! infor "Bayesian logistic regression"
	```math
	\begin{align}
	\text{Priors: }\;\;\;\;\;\;\beta_0 &\sim \mathcal{N}(m_0^{\beta_0}, v_0^{\beta_0})\\
	\boldsymbol{\beta}_1 &\sim \mathcal{N}(\mathbf{m}_0^{{\beta}_1}, \mathbf{V}_0^{{\beta}_1})\\
	\text{Likelihood: }\;\;\text{for } n &= 1,2,\ldots, N:\\
	\mu_n &=\beta_0 +  \boldsymbol{\beta}_1^\top\mathbf{x}_n \\
	\sigma_n &= \texttt{logistic}(\mu_n)\\
	y_n &\sim \texttt{Bernoulli}(\sigma_n).
	\end{align}
	```
"""

# ╔═╡ 8b73706e-fe00-4489-8095-b3ec4528c58b
md"""

### Implementation in `Julia`

Model translation is straightforward.
"""

# ╔═╡ 6d2af85d-8c9e-4da7-8a38-6c0df102f954
begin
	@model function bayesian_logistic_reg(X, y; v₀=10^2, V₀ = 10^2)
		# priors
		β0 ~ Normal(0, sqrt(v₀))
		nfeatures = size(X)[2]
		β ~ MvNormal(zeros(nfeatures), sqrt(V₀))
		# Likelihood
		μs = β0 .+ X * β
		# logistic transformations
		σs = logistic.(μs)
		for i in eachindex(y)
			y[i] ~ Bernoulli(σs[i])
		end
		return (; σs)
	end

end;

# ╔═╡ 8a8d8eb9-9cea-43f0-9607-9d3ca908c370
md"Next, we use `Turing` to do Bayesian logistic regression analysis on the toy data example introduced earlier."

# ╔═╡ 41a3984c-aee4-494f-8ba2-69c0274185ed
chain_logreg_sim_data = let 
	sample(
		bayesian_logistic_reg(D, targets; v₀=5^2),
		NUTS(),
		MCMCThreads(),
		2000,
		3
	)
end;

# ╔═╡ e1e43074-9e5f-4516-bf0d-0ce4209afb6c
summarystats(chain_logreg_sim_data)

# ╔═╡ 15b2d945-4e78-4c41-9712-5d623b15914e
describe(chain_logreg_sim_data)[2]

# ╔═╡ 5e5fdd62-ac1c-4ef6-a5a4-64ffe441b496
plot(chain_logreg_sim_data)

# ╔═╡ bdcc9726-d1fd-4d34-987e-925e1a96e58f
md"""

### Bayesian prediction
"""

# ╔═╡ fd9d6126-d764-40f5-9a4d-fda49a0962a9
md"""

To make a prediction at a new input location ``\mathbf{x}_\ast``, we can use the `predict()` or `generated_quantities()` method from `Turing`.

The procedure starts with initialising a `Turing` model with `missing` prediction targets ``\mathbf{y}_\ast``. Then use either `predict()` or `generated_quantities()` to find the Monte Carlo approximated prediction. Check the code below for an example.
"""

# ╔═╡ 69258680-fc21-40ca-998a-1a81279342ea
begin
	# randomly generated test dataset
	N_test = 5
	D_test = rand(N_test, 2) * 10
	pred_model = bayesian_logistic_reg(D_test, Vector{Union{Missing, Float64}}(undef, size(D_test)[1]))
	y_preds = predict(pred_model, chain_logreg_sim_data)
end;

# ╔═╡ be4d04ff-9ae8-40c6-ae7b-9ec29cd23b43
mixeddensity(y_preds[:,1:1,:], size(100,100))

# ╔═╡ a84e1f2f-fdde-432f-89d3-265480ef9f53
md"""
## Prediction comparison

"""

# ╔═╡ 6aaa775e-b2c4-4943-8860-9aff2e4a725c
md"""

### Why does Bayesian predict better?

Recall to make a prediction at a new input ``\mathbf{x}_\ast``, the Bayesian approach aims at computing its posterior (predictive) distribution, which is computed via an integration (and then approximated by the Monte Carlo method):

```math
\begin{align}
p_{\text{Bayes}}(y_\ast=1 |\mathbf{x}_\ast, \mathcal{D}) &= \int p(y_\ast=1|\boldsymbol{\beta})p(\boldsymbol{\beta}|\mathcal{D}) \mathrm{d}\boldsymbol{\beta}\\
&= \int \sigma_{\mathbf{x}_\ast}(\boldsymbol{\beta}) p(\boldsymbol{\beta}|\mathcal{D}) \mathrm{d}\boldsymbol{\beta}\\
&\approx \frac{1}{R} \sum_{r=1}^R \sigma^{(r)}_{\mathbf{x}_\ast},
\end{align}
```
where, to avoid cluttered notations, we have assumed ``\boldsymbol{\beta}^\top = [\beta_0, \boldsymbol{\beta}_1]``, and

```math
\sigma^{(r)}_{\mathbf{x}_\ast} = \frac{1}{1+\exp\{\beta^{(r)}_0 +\mathbf{x}_\ast^\top \boldsymbol{\beta}_1^{(r)}\}}.
```

Compared with the frequentist's point prediction

```math
p_{\text{freq}}(y_{\ast}=1|\mathbf{x}_\ast,  \hat{\boldsymbol{\beta}}) = \hat{\sigma}_{\mathbf{x}_\ast}(\hat{\boldsymbol{\beta}})= \frac{1}{1+\exp(- \hat\beta_0 - \mathbf{x}_\ast^\top\hat{\boldsymbol{\beta}}_1)},
```

the Bayesian prediction is an *ensemble* method. To be more specific, there are in total ``R`` predictions made based on the ``R`` MCMC samples ``\{\beta_0^{(r)}, \boldsymbol{\beta}_1^{(r)}\}_{r=1}^R``. And the Bayesian provides the final verdict by averaging over the ``R`` individual models. 

The idea is illustrated below in a figure in which the posterior prediction mean (thick green line) is plotted with some of the ensemble models (lighter grey lines). The Bayesian approach by averaging over multiple models provides a more reasonable over-fitting proof prediction.
"""

# ╔═╡ 68b88445-fb94-4d26-a723-234b3045ca54
begin
	p1_ = Plots.plot(D1[:,1], D1[:,2],  xlabel=L"$x_1$", ylabel=L"$x_2$", label="class 1", seriestype=:scatter, markersize = 4, legend = :outerright, title="Binary classification", xlim=[0, 11], ylim=[0, 9.5])
	Plots.plot!(p1_, D2[:,1], D2[:,2], label="class 2", seriestype=:scatter, markersize = 4)
	Plots.plot!(p1_, AB[1:1, 1], AB[1:1, 2], label="", seriestype=:scatter, markersize = 3, markershape =:x, annotate = [(AB[1,1]-0.8, AB[1,2], "A"), (AB[2,1]-0.8, AB[2,2], "B")], markerstrokewidth = 3, markercolor=:red)
	Plots.plot!(p1_, AB[2:2, 1], AB[2:2,2], seriestype=:scatter, label="", markersize = 3, markershape =:x, markerstrokewidth = 3, markercolor=:red)
	# Plots.plot!(size=(500,500))
end;

# ╔═╡ 39c43d27-6806-4fb6-a0e8-5f41ae0ee94e
md"""
## A real-world example

In this section, we apply Bayesian logistic regression analysis to a real-world dataset. The data used here is described in the book [Introduction to Statistical Learning](https://hastie.su.domains/ISLR2/ISLRv2_website.pdf). The dataset (referred to as `Default`) is about customer default records for a credit card company. 
"""

# ╔═╡ 436f0628-ee73-4045-82f3-6d785b5ba51f
md"""

#### Step 1: import the dataset
"""

# ╔═╡ e47c4ad6-17e4-4265-bee2-738b81e61696
md"""

#### Step 2: pre-process the dataset
"""

# ╔═╡ 8b56260f-2e42-4a89-a1c0-bf856b9f75d3
md"""
By checking the raw data, we find the `Default` and `Student` variables are of `string` type. We need to first transform them into binary data types.
"""

# ╔═╡ 40db5082-3558-4fd4-ab47-1127f6d67e38
begin
	# transform the non-numerical features to numerical 
	default_df[!, :DefaultNum] = map((x) -> x.Default == "Yes" ? true : false, eachrow(default_df))
	default_df[!, :StudentNum] = map((x) -> x.Student == "Yes" ? true : false, eachrow(default_df))
end;

# ╔═╡ fbcdbc4e-f55b-4bf8-a10d-42f2627dbfdb
describe(default_df)

# ╔═╡ 8c73a18f-55a1-4740-8795-5bbb6ff425de
md"The two numerical features `Balance` and `Income` are with very different mean and value ranges. It is in general a good idea to standardize them such that the transformed data are with zero mean and unit variance. By standardising the features, the prior's variances, *i.e. ``\mathbf{V}_0^{\boldsymbol{\beta}}``*, are also easier to be specified, since all the features are of the same scale.
"

# ╔═╡ 0ca3c752-627f-40ce-ac6c-d10fc90d4663
begin
	XX, yy = Matrix(default_df[!, [:Balance, :Income, :StudentNum]]), default_df[!, :DefaultNum]
	feature_scalar = fit(ZScoreTransform, XX[:, 1:2], dims=1)	
	XX[:, 1:2] .= StatsBase.transform(feature_scalar, XX[:, 1:2])
end;

# ╔═╡ a84de1b9-3c27-4b63-822f-f454b7d3098b
md"""

#### Step 4: making inference with `Turing`
"""

# ╔═╡ b25a3f92-f3ad-4c05-961d-2f69d39d98c3
md"It is, in general, a good idea to fit the data with the frequentist model first and use the estimation as a reference."

# ╔═╡ 4d9c1339-c38f-4705-9c00-2c99228da905
begin
	default_df_new = DataFrame([XX yy], [:Balance, :Income, :StudentNum, :Default])
	glm(@formula(Default ~ Balance +Income+StudentNum), default_df_new, Bernoulli(), LogitLink())
end

# ╔═╡ bd11a4c4-1f2b-4d3c-8e3f-8382dd9f3b3c
md"Next, we use the Bayesian logistic regression model implemented in `Turing` to do the inference."

# ╔═╡ 244ba3cf-63ba-4501-8e88-f71c95c15a7c
chain_default = let
	chain = sample(
		bayesian_logistic_reg(XX, yy; v₀=1, V₀ =1),
		NUTS(),
		MCMCThreads(),
		2000,
		3
	)
	replacenames(chain,  Dict(["β[1]" => "Balance", "β[2]" => "Income", "β[3]" => "Student"]))
end;

# ╔═╡ c83f3735-6aba-4183-b010-5f21cd2ff968
describe(chain_default)[1]

# ╔═╡ 30d1520d-d301-422a-81e1-a40122d5e3fa
md"It can be observed that the Bayesian inference's posterior means are similar to the frequentist's estimation, which implies our prior choice is reasonably weak."

# ╔═╡ 53c5b238-61fd-4ef3-9194-b076b3434b16
describe(chain_default)[2]

# ╔═╡ 0c34decf-ee35-4f9d-bf83-cfff75f8ff3b
md"The Bayesian's credible interval also tells us the intercept, `Balance`, and `Student` are significant predictors (their 95% credible intervals are either strictly positive or negative). But `Income` factor's impact on predicting the log-ratio of `Default` is not statistically significant, which is in agreement with the Frequentist's analysis. The same result can also be observed from the density plots."

# ╔═╡ f092a42e-16e9-45ac-88cd-133a92402ff6
plot(chain_default)

# ╔═╡ 59245146-ef30-4df1-9ac3-776871e5d062
md"""
## Appendix

"""

# ╔═╡ ea897f9a-89ff-421c-989a-b5f395cec705
begin
	prediction(ws, x1, x2) = mean(logistic.(ws * [1.0, x1, x2]))
end

# ╔═╡ 78d6fe62-432b-49f3-b38f-0f6f6f5a04ed
chain_array = let
	model_ex1 = bayesian_logistic_reg(D, targets)
	Random.seed!(100)
	chain=sample(model_ex1, NUTS(), 1000, discard_initial=100, thinning=10)
	Array(chain)
end;

# ╔═╡ 2a632fe1-698f-4265-8509-453ee7827ae6
let

	p_bayes_pred = Plots.plot(D1[:, 1], D1[:,2], seriestype=:scatter, markersize = 5, markercolor=1, label="class 1", legend=:topright, xlim=[-1, 11], ylim=[-1,11])
	Plots.plot!(p_bayes_pred, D2[:, 1], D2[:,2], seriestype=:scatter, markersize = 5,  markercolor=2, label="class 2")
	mean_pred = mean(chain_array, dims=1)[:]

	b, k =  -chain_array[1, 1:2] ./	chain_array[1, 3]
	plot!(-2:12, (x) -> k*x+b,  lw=0.1, lc=:gray, label=L"\sigma^{(r)}\sim p(\sigma|\mathcal{D})")
	for i in 2:60
		b, k =  -chain_array[i, 1:2] ./	chain_array[i, 3]
		plot!(-2:12, (x) -> k*x+b,  lw=0.1, lc=:gray, label="")
	end
	b, k =  - mean_pred[1:2] ./	mean_pred[3]
	plot!(-2:12, (x) -> k*x+b,  lw=3, lc=3, label=L"\texttt{mean}(\sigma^{(r)})")
	p_bayes_pred

end

# ╔═╡ c92f0602-9a6c-4e2c-8a28-2a870d332fe4
begin
	p1 = Plots.plot(D1[:,1], D1[:,2],  xlabel=L"x_1", ylabel=L"x_2", label="class 1", seriestype=:scatter, markersize = 4, legend = :bottomright, title="Binary classification", ratio =1.0)
	Plots.plot!(p1, D2[:,1], D2[:,2], label="class 2", seriestype=:scatter, markersize = 4)
	# plot!((x)-> -x, lw=4, lc=:gray, label="Decision boundary", ls=:dash, legend=:outerright)
end;

# ╔═╡ f42b1665-df4b-4181-be03-71ccc3dbfae2
md"""

In a supervised learning setting, we are predicting the target ``y_n`` based on ``n``-the sample's features ``\mathbf{x}_n``.  
For example, in regression analysis, the target or labels ``y_n`` are assumed to be real-valued, i.e. ``y_n\in \mathbb{R}``. For example, in the ```Advertising``` example, the target ```sales``` of a particular problem is real-valued. 


The targets ``y_n``, however, can take value other than the real number. For example, a very common example is ``y_n`` can take binary choices, say ``y_n \in \{\texttt{true}, \texttt{false}\}``. Such a supervised learning task is usually referred to as *binary* **classification**. For example, given a subject's age, gender, and other measurements, how likely he/she will survive a pandemic?  The outcome is binary here: either survive or not. Also, check the following plot for an example of binary classification with 2-dimensional input.

$(begin
p1
end)


A popular statistical model for binary classification is *logistic regression*, in which we aim at drawing a linear decision boundary to classify the input (as shown in the figure above). In this chapter, we are going to investigate how to do Bayesian logistic regression. We will first review the frequentist's logistic model and then extends it to a Bayesian approach. The two approaches will be compared and the benefit of the Bayesian approach should become evident when we compare their prediction on unseen input data.
"""

# ╔═╡ 82fc962c-a172-47ef-a86c-fa49bace3567
p_freq_1= let
	freq_coef = coef(glm_fit)'
	# prediction(ws, x1, x2) = logistic(ws * [1.0, x1, x2])
	p_freq_1 = Plots.contour(2:0.1:9, 2:0.1:8, (x, y) -> prediction(freq_coef, x, y), fill=false, connectgaps=true, levels=8, line_smoothing = 0.85, legend=:left, title="Frequentist Prediction", c=:roma, ratio=1.0, xlabel=L"x_1", ylabel=L"x_2")
	Plots.plot!(p_freq_1, D1[:, 1], D1[:,2], seriestype=:scatter, markersize = 3, markercolor=1, label="class 1")
	Plots.plot!(p_freq_1, D2[:, 1], D2[:,2], seriestype=:scatter, markersize = 3,  markercolor=2, label="class 2")
	Plots.plot!(p_freq_1, AB[1:2, 1], AB[1:2, 2], label="", seriestype=:scatter, markersize = 2, markershape =:star4, annotate = [(AB[1,1], AB[1,2], text("A", :top,:red, 9)), (AB[2,1], AB[2,2], text("B", :top, :red, 9))], markerstrokewidth = 1, markercolor=:red)
	markers = [2, 5, 6, 9]
	for m in markers
		p0 = round(prediction(freq_coef, D[m, 1], D[m, 2]), digits=2)
		annotate!(D[m, 1], D[m,2], text(L"\hat{\sigma}="*"$(p0)", :bottom, 10))
	end

	for i in 1:2
		p0 = round(prediction(freq_coef, AB[i, 1], AB[i, 2]), digits=2)
		annotate!(AB[i, 1], AB[i,2], text(L"\hat{\sigma}="*"$(p0)", :bottom, :red, 10))
	end
	p_freq_1
end;

# ╔═╡ cd76fa94-d0d7-43bb-8221-2a4dafa8af53
p_freq_1

# ╔═╡ 3e45f16f-ea6c-4960-98b7-1e642fb919c1
p_bayes_1 = let
	p_bayes_1 = Plots.contour(2:0.1:9, 2:0.1:8, (x, y) -> prediction(chain_array, x, y), fill=false, connectgaps=true, levels=8, line_smoothing = 0.85, legend=:left, title="Bayesian Prediction", c=:roma, ratio=1.0, xlabel=L"x_1", ylabel=L"x_2")
	Plots.plot!(p_bayes_1, D1[:, 1], D1[:,2], seriestype=:scatter, markersize = 3, markercolor=1, label="class 1")
	Plots.plot!(p_bayes_1, D2[:, 1], D2[:,2], seriestype=:scatter, markersize = 3,  markercolor=2, label="class 2")
	Plots.plot!(p_bayes_1, AB[1:2, 1], AB[1:2, 2], label="", seriestype=:scatter, markersize = 2, markershape =:star4, annotate = [(AB[1,1], AB[1,2], text("A", :top,:red, 9)), (AB[2,1], AB[2,2], text("B", :top, :red, 9))], markerstrokewidth = 1, markercolor=:red)
	markers = [2, 5, 6, 9]
	for m in markers
		p0 = round(prediction(chain_array, D[m, 1], D[m, 2]), digits=2)
		annotate!(D[m, 1], D[m,2], text(L"\hat{\sigma}="*"$(p0)", :bottom, 10))
	end

	for i in 1:2
		p0 = round(prediction(chain_array, AB[i, 1], AB[i, 2]), digits=2)
		annotate!(AB[i, 1], AB[i,2], text(L"\hat{\sigma}="*"$(p0)", :bottom, :red, 10))
	end
	p_bayes_1
end;

# ╔═╡ 44ccb675-a657-4fe8-934f-ddf29cb78f74
md"""

We have discussed the undesired properties of the Frequentist's method. The prediction lack nuance to account for the differences between the prediction locations. The prediction is very black and white: all data points are either predicted with 100% or 0% being positive. 


Now we move on to check what the Bayesian prediction surface looks like. Recall that Bayesian inference always aims at computing the posterior of the quantity of interest. In this case, what we are interested in is the predictive distribution on a new input location ``\mathbf{x}_\ast``:

```math
p(y_\ast=1|\mathbf{x}_\ast, \mathcal{D}).
```
The contour plot of the Bayesian predictive distribution is listed below.

$(begin
p_bayes_1
end)

It can be observed that the Bayesian prediction is more nuanced compared with the clean-cut frequentist's prediction.
* data points closer to the decision boundary are correctly predicted with less confidence
* data points located further away from the observed input data are predicted with some reasonable level of uncertainty.

The surface plots of the two predictions are listed below for a more direct visual comparison. The Bayesian prediction is more natural and matches people's expectations.
"""

# ╔═╡ 8a21c570-9bfe-4f66-9157-1b0dc4028ef4
p_freq_surface_1 = let
	freq_coef = coef(glm_fit)'
	Plots.surface(0:0.1:10, 0:0.1:10, (x, y) -> prediction(freq_coef, x, y), legend=:best, title="Frequentist Prediction", c=:roma, ratio=1.0, xlabel=L"x_1", ylabel=L"x_2", zlabel=L"p(y=1|\ldots)")
end;

# ╔═╡ 0c70c6be-518b-4ba4-bd69-cc34d2217077
p_freq_surface_1

# ╔═╡ f9b3916a-d4b2-4e6b-9a7d-be077fd45ac0
p_bayes_surface_1 = let
	Plots.surface(0:0.1:10, 0:0.1:10, (x, y) -> prediction(chain_array, x, y), legend=:best, title="Bayesian Prediction", c=:roma, ratio=1.0, xlabel=L"x_1", ylabel=L"x_2", zlabel=L"p(y=1|\ldots)")
end;

# ╔═╡ 922704a0-b0c9-4fe0-a0fb-3ab58a7f01d9
plot(p_freq_surface_1, p_bayes_surface_1, size=(800,400))

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
GLM = "38e38edf-8417-5370-95a0-9cbb8c7f171a"
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
RDatasets = "ce6b1742-4840-55fa-b093-852dadbb1d8b"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

[compat]
DataFrames = "~1.3.4"
GLM = "~1.8.0"
LaTeXStrings = "~1.3.0"
Plots = "~1.40.8"
PlutoUI = "~0.7.39"
RDatasets = "~0.7.7"
StatsBase = "~0.34.3"
StatsFuns = "~1.3.0"
StatsPlots = "~0.15.1"
Turing = "~0.34.1"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

julia_version = "1.11.0"
manifest_format = "2.0"
project_hash = "1dcdbf5079b89822ff3c58129edd7898184ff907"

[[deps.ADTypes]]
git-tree-sha1 = "eea5d80188827b35333801ef97a40c2ed653b081"
uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
version = "1.9.0"

    [deps.ADTypes.extensions]
    ADTypesChainRulesCoreExt = "ChainRulesCore"
    ADTypesEnzymeCoreExt = "EnzymeCore"

    [deps.ADTypes.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"

[[deps.AbstractFFTs]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.5.0"
weakdeps = ["ChainRulesCore", "Test"]

    [deps.AbstractFFTs.extensions]
    AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
    AbstractFFTsTestExt = "Test"

[[deps.AbstractMCMC]]
deps = ["BangBang", "ConsoleProgressMonitor", "Distributed", "FillArrays", "LogDensityProblems", "Logging", "LoggingExtras", "ProgressLogging", "Random", "StatsBase", "TerminalLoggers", "Transducers"]
git-tree-sha1 = "c732dd9f356d26cc48d3b484f3fd9886c0ba8ba3"
uuid = "80f14c24-f653-4e6a-9b94-39d6b0f70001"
version = "5.5.0"

[[deps.AbstractPPL]]
deps = ["AbstractMCMC", "Accessors", "DensityInterface", "Random"]
git-tree-sha1 = "6380a9a03a4207bac53ac310dd3a283bb4df54ef"
uuid = "7a57a42e-76ec-4ea3-a279-07e840d6d9cf"
version = "0.8.4"

[[deps.AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "6e1d2a35f2f90a4bc7c2ed98079b2ba09c35b83a"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.3.2"

[[deps.AbstractTrees]]
git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.4.5"

[[deps.Accessors]]
deps = ["CompositionsBase", "ConstructionBase", "InverseFunctions", "LinearAlgebra", "MacroTools", "Markdown"]
git-tree-sha1 = "b392ede862e506d451fc1616e79aa6f4c673dab8"
uuid = "7d9f7c33-5ae7-4f3b-8dc6-eff91059b697"
version = "0.1.38"

    [deps.Accessors.extensions]
    AccessorsAxisKeysExt = "AxisKeys"
    AccessorsDatesExt = "Dates"
    AccessorsIntervalSetsExt = "IntervalSets"
    AccessorsStaticArraysExt = "StaticArrays"
    AccessorsStructArraysExt = "StructArrays"
    AccessorsTestExt = "Test"
    AccessorsUnitfulExt = "Unitful"

    [deps.Accessors.weakdeps]
    AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
    Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
    IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
    Requires = "ae029012-a4dd-5104-9daa-d747884805df"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.Adapt]]
deps = ["LinearAlgebra", "Requires"]
git-tree-sha1 = "6a55b747d1812e699320963ffde36f1ebdda4099"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "4.0.4"
weakdeps = ["StaticArrays"]

    [deps.Adapt.extensions]
    AdaptStaticArraysExt = "StaticArrays"

[[deps.AdvancedHMC]]
deps = ["AbstractMCMC", "ArgCheck", "DocStringExtensions", "InplaceOps", "LinearAlgebra", "LogDensityProblems", "LogDensityProblemsAD", "ProgressMeter", "Random", "Requires", "Setfield", "SimpleUnPack", "Statistics", "StatsBase", "StatsFuns"]
git-tree-sha1 = "1da0961a400c28d1e5f057e922ff75ec5d6a5747"
uuid = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
version = "0.6.2"

    [deps.AdvancedHMC.extensions]
    AdvancedHMCCUDAExt = "CUDA"
    AdvancedHMCMCMCChainsExt = "MCMCChains"
    AdvancedHMCOrdinaryDiffEqExt = "OrdinaryDiffEq"

    [deps.AdvancedHMC.weakdeps]
    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
    MCMCChains = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
    OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"

[[deps.AdvancedMH]]
deps = ["AbstractMCMC", "Distributions", "FillArrays", "LinearAlgebra", "LogDensityProblems", "Random", "Requires"]
git-tree-sha1 = "66ac4c7b320d2434f04d48116db02e73e6dabc8b"
uuid = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
version = "0.8.3"
weakdeps = ["DiffResults", "ForwardDiff", "MCMCChains", "StructArrays"]

    [deps.AdvancedMH.extensions]
    AdvancedMHForwardDiffExt = ["DiffResults", "ForwardDiff"]
    AdvancedMHMCMCChainsExt = "MCMCChains"
    AdvancedMHStructArraysExt = "StructArrays"

[[deps.AdvancedPS]]
deps = ["AbstractMCMC", "Distributions", "Random", "Random123", "Requires", "SSMProblems", "StatsFuns"]
git-tree-sha1 = "5dcd3de7e7346f48739256e71a86d0f96690b8c8"
uuid = "576499cb-2369-40b2-a588-c64705576edc"
version = "0.6.0"
weakdeps = ["Libtask"]

    [deps.AdvancedPS.extensions]
    AdvancedPSLibtaskExt = "Libtask"

[[deps.AdvancedVI]]
deps = ["ADTypes", "Bijectors", "DiffResults", "Distributions", "DistributionsAD", "DocStringExtensions", "ForwardDiff", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "StatsBase", "StatsFuns", "Tracker"]
git-tree-sha1 = "c217a9b531b4b752eb120a9f820527126ba68fb9"
uuid = "b5ca4192-6429-45e5-a2d9-87aec30a685c"
version = "0.2.8"

    [deps.AdvancedVI.extensions]
    AdvancedVIEnzymeExt = ["Enzyme"]
    AdvancedVIFluxExt = ["Flux"]
    AdvancedVIReverseDiffExt = ["ReverseDiff"]
    AdvancedVIZygoteExt = ["Zygote"]

    [deps.AdvancedVI.weakdeps]
    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
    Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.AliasTables]]
deps = ["PtrArrays", "Random"]
git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
version = "1.1.3"

[[deps.ArgCheck]]
git-tree-sha1 = "a3a402a35a2f7e0b87828ccabbd5ebfbebe356b4"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.3.0"

[[deps.ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.2"

[[deps.ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "d57bd3762d308bded22c3b82d033bff85f6195c6"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.4.0"

[[deps.Arpack]]
deps = ["Arpack_jll", "Libdl", "LinearAlgebra", "Logging"]
git-tree-sha1 = "9b9b347613394885fd1c8c7729bfc60528faa436"
uuid = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
version = "0.5.4"

[[deps.Arpack_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg"]
git-tree-sha1 = "5ba6c757e8feccf03a1554dfaf3e26b3cfc7fd5e"
uuid = "68821587-b530-5797-8361-c406ea357684"
version = "3.5.1+1"

[[deps.ArrayInterface]]
deps = ["Adapt", "LinearAlgebra"]
git-tree-sha1 = "3640d077b6dafd64ceb8fd5c1ec76f7ca53bcf76"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "7.16.0"

    [deps.ArrayInterface.extensions]
    ArrayInterfaceBandedMatricesExt = "BandedMatrices"
    ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
    ArrayInterfaceCUDAExt = "CUDA"
    ArrayInterfaceCUDSSExt = "CUDSS"
    ArrayInterfaceChainRulesExt = "ChainRules"
    ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
    ArrayInterfaceReverseDiffExt = "ReverseDiff"
    ArrayInterfaceSparseArraysExt = "SparseArrays"
    ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
    ArrayInterfaceTrackerExt = "Tracker"

    [deps.ArrayInterface.weakdeps]
    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
    CUDSS = "45b445bb-4962-46a0-9369-b4df9d0f772e"
    ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
    GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"

[[deps.Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
version = "1.11.0"

[[deps.Atomix]]
deps = ["UnsafeAtomics"]
git-tree-sha1 = "c06a868224ecba914baa6942988e2f2aade419be"
uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458"
version = "0.1.0"

[[deps.AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "01b8ccb13d68535d73d2b0c23e39bd23155fb712"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.1.0"

[[deps.AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "16351be62963a67ac4083f748fdb3cca58bfd52f"
uuid = "39de3d68-74b9-583c-8d2d-e117c070f3a9"
version = "0.4.7"

[[deps.BangBang]]
deps = ["Accessors", "ConstructionBase", "InitialValues", "LinearAlgebra", "Requires"]
git-tree-sha1 = "e2144b631226d9eeab2d746ca8880b7ccff504ae"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.4.3"

    [deps.BangBang.extensions]
    BangBangChainRulesCoreExt = "ChainRulesCore"
    BangBangDataFramesExt = "DataFrames"
    BangBangStaticArraysExt = "StaticArrays"
    BangBangStructArraysExt = "StructArrays"
    BangBangTablesExt = "Tables"
    BangBangTypedTablesExt = "TypedTables"

    [deps.BangBang.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
    StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
    Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
    TypedTables = "9d95f2ec-7b3d-5a63-8d20-e2491e220bb9"

[[deps.Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
version = "1.11.0"

[[deps.Baselet]]
git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
version = "0.1.1"

[[deps.Bijections]]
git-tree-sha1 = "d8b0439d2be438a5f2cd68ec158fe08a7b2595b7"
uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
version = "0.1.9"

[[deps.Bijectors]]
deps = ["ArgCheck", "ChainRules", "ChainRulesCore", "ChangesOfVariables", "Compat", "Distributions", "DocStringExtensions", "Functors", "InverseFunctions", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "MappedArrays", "Random", "Reexport", "Requires", "Roots", "SparseArrays", "Statistics"]
git-tree-sha1 = "92edc3544607c4fda1b30357910597e2a70dc5ea"
uuid = "76274a88-744f-5084-9051-94815aaf08c4"
version = "0.13.18"

    [deps.Bijectors.extensions]
    BijectorsDistributionsADExt = "DistributionsAD"
    BijectorsEnzymeExt = "Enzyme"
    BijectorsForwardDiffExt = "ForwardDiff"
    BijectorsLazyArraysExt = "LazyArrays"
    BijectorsReverseDiffExt = "ReverseDiff"
    BijectorsTapirExt = "Tapir"
    BijectorsTrackerExt = "Tracker"
    BijectorsZygoteExt = "Zygote"

    [deps.Bijectors.weakdeps]
    DistributionsAD = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    Tapir = "07d77754-e150-4737-8c94-cd238a1fb45b"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.BitFlags]]
git-tree-sha1 = "0691e34b3bb8be9307330f88d1a3c3f25466c24d"
uuid = "d1d4a3ce-64b1-5f1a-9ba4-7e7e69966f35"
version = "0.1.9"

[[deps.Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+1"

[[deps.CEnum]]
git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
version = "0.5.0"

[[deps.CSV]]
deps = ["CodecZlib", "Dates", "FilePathsBase", "InlineStrings", "Mmap", "Parsers", "PooledArrays", "PrecompileTools", "SentinelArrays", "Tables", "Unicode", "WeakRefStrings", "WorkerUtilities"]
git-tree-sha1 = "6c834533dc1fabd820c1db03c839bf97e45a3fab"
uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
version = "0.10.14"

[[deps.Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "009060c9a6168704143100f36ab08f06c2af4642"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.18.2+1"

[[deps.CategoricalArrays]]
deps = ["DataAPI", "Future", "Missings", "Printf", "Requires", "Statistics", "Unicode"]
git-tree-sha1 = "1568b28f91293458345dabba6a5ea3f183250a61"
uuid = "324d7699-5711-5eae-9e2f-1d82baa6b597"
version = "0.10.8"

    [deps.CategoricalArrays.extensions]
    CategoricalArraysJSONExt = "JSON"
    CategoricalArraysRecipesBaseExt = "RecipesBase"
    CategoricalArraysSentinelArraysExt = "SentinelArrays"
    CategoricalArraysStructTypesExt = "StructTypes"

    [deps.CategoricalArrays.weakdeps]
    JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
    RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
    SentinelArrays = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
    StructTypes = "856f2bd8-1eba-4b0a-8007-ebc267875bd4"

[[deps.ChainRules]]
deps = ["Adapt", "ChainRulesCore", "Compat", "Distributed", "GPUArraysCore", "IrrationalConstants", "LinearAlgebra", "Random", "RealDot", "SparseArrays", "SparseInverseSubset", "Statistics", "StructArrays", "SuiteSparse"]
git-tree-sha1 = "be227d253d132a6d57f9ccf5f67c0fb6488afd87"
uuid = "082447d4-558c-5d27-93f4-14fc19e9eca2"
version = "1.71.0"

[[deps.ChainRulesCore]]
deps = ["Compat", "LinearAlgebra"]
git-tree-sha1 = "3e4b134270b372f2ed4d4d0e936aabaefc1802bc"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.25.0"
weakdeps = ["SparseArrays"]

    [deps.ChainRulesCore.extensions]
    ChainRulesCoreSparseArraysExt = "SparseArrays"

[[deps.ChangesOfVariables]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "799b25ca3a8a24936ae7b5c52ad194685fc3e6ef"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.9"
weakdeps = ["InverseFunctions", "Test"]

    [deps.ChangesOfVariables.extensions]
    ChangesOfVariablesInverseFunctionsExt = "InverseFunctions"
    ChangesOfVariablesTestExt = "Test"

[[deps.Clustering]]
deps = ["Distances", "LinearAlgebra", "NearestNeighbors", "Printf", "Random", "SparseArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "9ebb045901e9bbf58767a9f34ff89831ed711aae"
uuid = "aaaa29a8-35af-508c-8bc3-b662a17a0fe5"
version = "0.15.7"

[[deps.CodecZlib]]
deps = ["TranscodingStreams", "Zlib_jll"]
git-tree-sha1 = "bce6804e5e6044c6daab27bb533d1295e4a2e759"
uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
version = "0.7.6"

[[deps.ColorSchemes]]
deps = ["ColorTypes", "ColorVectorSpace", "Colors", "FixedPointNumbers", "PrecompileTools", "Random"]
git-tree-sha1 = "b5278586822443594ff615963b0c09755771b3e0"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.26.0"

[[deps.ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "b10d0b65641d57b8b4d5e234446582de5047050d"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.5"

[[deps.ColorVectorSpace]]
deps = ["ColorTypes", "FixedPointNumbers", "LinearAlgebra", "Requires", "Statistics", "TensorCore"]
git-tree-sha1 = "a1f44953f2382ebb937d60dafbe2deea4bd23249"
uuid = "c3611d14-8923-5661-9e6a-0046d554d3a4"
version = "0.10.0"
weakdeps = ["SpecialFunctions"]

    [deps.ColorVectorSpace.extensions]
    SpecialFunctionsExt = "SpecialFunctions"

[[deps.Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "362a287c3aa50601b0bc359053d5c2468f0e7ce0"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.11"

[[deps.Combinatorics]]
git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
version = "1.0.2"

[[deps.CommonSolve]]
git-tree-sha1 = "0eee5eb66b1cf62cd6ad1b460238e60e4b09400c"
uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
version = "0.2.4"

[[deps.CommonSubexpressions]]
deps = ["MacroTools"]
git-tree-sha1 = "cda2cfaebb4be89c9084adaca7dd7333369715c5"
uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
version = "0.3.1"

[[deps.CommonWorldInvalidations]]
git-tree-sha1 = "ae52d1c52048455e85a387fbee9be553ec2b68d0"
uuid = "f70d9fcc-98c5-4d4a-abd7-e4cdeebd8ca8"
version = "1.0.0"

[[deps.Compat]]
deps = ["TOML", "UUIDs"]
git-tree-sha1 = "8ae8d32e09f0dcf42a36b90d4e17f5dd2e4c4215"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "4.16.0"
weakdeps = ["Dates", "LinearAlgebra"]

    [deps.Compat.extensions]
    CompatLinearAlgebraExt = "LinearAlgebra"

[[deps.CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
version = "1.1.1+0"

[[deps.CompositeTypes]]
git-tree-sha1 = "bce26c3dab336582805503bed209faab1c279768"
uuid = "b152e2b5-7a66-4b01-a709-34e65c35f657"
version = "0.1.4"

[[deps.CompositionsBase]]
git-tree-sha1 = "802bb88cd69dfd1509f6670416bd4434015693ad"
uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
version = "0.1.2"
weakdeps = ["InverseFunctions"]

    [deps.CompositionsBase.extensions]
    CompositionsBaseInverseFunctionsExt = "InverseFunctions"

[[deps.ConcurrentUtilities]]
deps = ["Serialization", "Sockets"]
git-tree-sha1 = "ea32b83ca4fefa1768dc84e504cc0a94fb1ab8d1"
uuid = "f0e56b4a-5159-44fe-b623-3e5288b988bb"
version = "2.4.2"

[[deps.ConsoleProgressMonitor]]
deps = ["Logging", "ProgressMeter"]
git-tree-sha1 = "3ab7b2136722890b9af903859afcf457fa3059e8"
uuid = "88cd18e8-d9cc-4ea6-8889-5259c0d15c8b"
version = "0.1.2"

[[deps.ConstructionBase]]
git-tree-sha1 = "76219f1ed5771adbb096743bff43fb5fdd4c1157"
uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
version = "1.5.8"
weakdeps = ["IntervalSets", "LinearAlgebra", "StaticArrays"]

    [deps.ConstructionBase.extensions]
    ConstructionBaseIntervalSetsExt = "IntervalSets"
    ConstructionBaseLinearAlgebraExt = "LinearAlgebra"
    ConstructionBaseStaticArraysExt = "StaticArrays"

[[deps.Contour]]
git-tree-sha1 = "439e35b0b36e2e5881738abc8857bd92ad6ff9a8"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.6.3"

[[deps.Crayons]]
git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
version = "4.1.1"

[[deps.DSP]]
deps = ["Compat", "FFTW", "IterTools", "LinearAlgebra", "Polynomials", "Random", "Reexport", "SpecialFunctions", "Statistics"]
git-tree-sha1 = "0df00546373af8eee1598fb4b2ba480b1ebe895c"
uuid = "717857b8-e6f2-59f4-9121-6e50c889abd2"
version = "0.7.10"

[[deps.DataAPI]]
git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.16.0"

[[deps.DataFrames]]
deps = ["Compat", "DataAPI", "Future", "InvertedIndices", "IteratorInterfaceExtensions", "LinearAlgebra", "Markdown", "Missings", "PooledArrays", "PrettyTables", "Printf", "REPL", "Reexport", "SortingAlgorithms", "Statistics", "TableTraits", "Tables", "Unicode"]
git-tree-sha1 = "db2a9cb664fcea7836da4b414c3278d71dd602d2"
uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
version = "1.3.6"

[[deps.DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "1d0a14036acb104d9e89698bd408f63ab58cdc82"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.20"

[[deps.DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[deps.Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
version = "1.11.0"

[[deps.Dbus_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl"]
git-tree-sha1 = "fc173b380865f70627d7dd1190dc2fce6cc105af"
uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab"
version = "1.14.10+0"

[[deps.DefineSingletons]]
git-tree-sha1 = "0fba8b706d0178b4dc7fd44a96a92382c9065c2c"
uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52"
version = "0.1.2"

[[deps.DelimitedFiles]]
deps = ["Mmap"]
git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
version = "1.9.1"

[[deps.DensityInterface]]
deps = ["InverseFunctions", "Test"]
git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
version = "0.4.0"

[[deps.Dictionaries]]
deps = ["Indexing", "Random", "Serialization"]
git-tree-sha1 = "35b66b6744b2d92c778afd3a88d2571875664a2a"
uuid = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
version = "0.4.2"

[[deps.DiffResults]]
deps = ["StaticArraysCore"]
git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621"
uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
version = "1.1.0"

[[deps.DiffRules]]
deps = ["IrrationalConstants", "LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
git-tree-sha1 = "23163d55f885173722d1e4cf0f6110cdbaf7e272"
uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
version = "1.15.1"

[[deps.Distances]]
deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0"
uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
version = "0.10.11"
weakdeps = ["ChainRulesCore", "SparseArrays"]

    [deps.Distances.extensions]
    DistancesChainRulesCoreExt = "ChainRulesCore"
    DistancesSparseArraysExt = "SparseArrays"

[[deps.Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
version = "1.11.0"

[[deps.Distributions]]
deps = ["AliasTables", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns"]
git-tree-sha1 = "d7477ecdafb813ddee2ae727afa94e9dcb5f3fb0"
uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
version = "0.25.112"
weakdeps = ["ChainRulesCore", "DensityInterface", "Test"]

    [deps.Distributions.extensions]
    DistributionsChainRulesCoreExt = "ChainRulesCore"
    DistributionsDensityInterfaceExt = "DensityInterface"
    DistributionsTestExt = "Test"

[[deps.DistributionsAD]]
deps = ["Adapt", "ChainRules", "ChainRulesCore", "Compat", "Distributions", "FillArrays", "LinearAlgebra", "PDMats", "Random", "Requires", "SpecialFunctions", "StaticArrays", "StatsFuns", "ZygoteRules"]
git-tree-sha1 = "02c2e6e6a137069227439fe884d729cca5b70e56"
uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
version = "0.6.57"

    [deps.DistributionsAD.extensions]
    DistributionsADForwardDiffExt = "ForwardDiff"
    DistributionsADLazyArraysExt = "LazyArrays"
    DistributionsADReverseDiffExt = "ReverseDiff"
    DistributionsADTrackerExt = "Tracker"

    [deps.DistributionsAD.weakdeps]
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"

[[deps.DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.9.3"

[[deps.DomainSets]]
deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "490392af2c7d63183bfa2c8aaa6ab981c5ba7561"
uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
version = "0.7.14"

    [deps.DomainSets.extensions]
    DomainSetsMakieExt = "Makie"

    [deps.DomainSets.weakdeps]
    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"

[[deps.Downloads]]
deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
version = "1.6.0"

[[deps.DynamicPPL]]
deps = ["ADTypes", "AbstractMCMC", "AbstractPPL", "Accessors", "BangBang", "Bijectors", "Compat", "ConstructionBase", "Distributions", "DocStringExtensions", "LinearAlgebra", "LogDensityProblems", "LogDensityProblemsAD", "MacroTools", "OrderedCollections", "Random", "Requires", "Test"]
git-tree-sha1 = "6e5aa7546a0281a1b4bb51a26d0145bb92813a34"
uuid = "366bfd00-2699-11ea-058f-f148b4cae6d8"
version = "0.28.5"

    [deps.DynamicPPL.extensions]
    DynamicPPLChainRulesCoreExt = ["ChainRulesCore"]
    DynamicPPLEnzymeCoreExt = ["EnzymeCore"]
    DynamicPPLForwardDiffExt = ["ForwardDiff"]
    DynamicPPLMCMCChainsExt = ["MCMCChains"]
    DynamicPPLReverseDiffExt = ["ReverseDiff"]
    DynamicPPLZygoteRulesExt = ["ZygoteRules"]

    [deps.DynamicPPL.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    MCMCChains = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    ZygoteRules = "700de1a5-db45-46bc-99cf-38207098b444"

[[deps.DynamicPolynomials]]
deps = ["Future", "LinearAlgebra", "MultivariatePolynomials", "MutableArithmetics", "Reexport", "Test"]
git-tree-sha1 = "bbf1ace0781d9744cb697fb856bd2c3f6568dadb"
uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
version = "0.6.0"

[[deps.Einsum]]
deps = ["Compat"]
git-tree-sha1 = "4a6b3eee0161c89700b6c1949feae8b851da5494"
uuid = "b7d42ee7-0b51-5a75-98ca-779d3107e4c0"
version = "0.4.1"

[[deps.EllipticalSliceSampling]]
deps = ["AbstractMCMC", "ArrayInterface", "Distributions", "Random", "Statistics"]
git-tree-sha1 = "e611b7fdfbfb5b18d5e98776c30daede41b44542"
uuid = "cad2338a-1db2-11e9-3401-43bc07c9ede2"
version = "2.0.0"

[[deps.EnumX]]
git-tree-sha1 = "bdb1942cd4c45e3c678fd11569d5cccd80976237"
uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
version = "1.0.4"

[[deps.EpollShim_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8e9441ee83492030ace98f9789a654a6d0b1f643"
uuid = "2702e6a9-849d-5ed8-8c21-79e8b8f9ee43"
version = "0.0.20230411+0"

[[deps.ExceptionUnwrapping]]
deps = ["Test"]
git-tree-sha1 = "dcb08a0d93ec0b1cdc4af184b26b591e9695423a"
uuid = "460bff9d-24e4-43bc-9d9f-a8973cb893f4"
version = "0.1.10"

[[deps.Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1c6317308b9dc757616f0b5cb379db10494443a7"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.6.2+0"

[[deps.ExprTools]]
git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
version = "0.1.10"

[[deps.Expronicon]]
deps = ["MLStyle", "Pkg", "TOML"]
git-tree-sha1 = "fc3951d4d398b5515f91d7fe5d45fc31dccb3c9b"
uuid = "6b7a57c9-7cc1-4fdf-b7f5-e857abae3636"
version = "0.8.5"

[[deps.FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "53ebe7511fa11d33bec688a9178fac4e49eeee00"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.2"

[[deps.FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "PCRE2_jll", "Zlib_jll", "libaom_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "466d45dc38e15794ec7d5d63ec03d776a9aff36e"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.4+1"

[[deps.FFTW]]
deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
git-tree-sha1 = "4820348781ae578893311153d69049a93d05f39d"
uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
version = "1.8.0"

[[deps.FFTW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4d81ed14783ec49ce9f2e168208a12ce1815aa25"
uuid = "f5851436-0d7a-5f13-b9de-f02708fd171a"
version = "3.3.10+1"

[[deps.FileIO]]
deps = ["Pkg", "Requires", "UUIDs"]
git-tree-sha1 = "62ca0547a14c57e98154423419d8a342dca75ca9"
uuid = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
version = "1.16.4"

[[deps.FilePathsBase]]
deps = ["Compat", "Dates"]
git-tree-sha1 = "7878ff7172a8e6beedd1dea14bd27c3c6340d361"
uuid = "48062228-2e41-5def-b9a4-89aafe57970f"
version = "0.9.22"
weakdeps = ["Mmap", "Test"]

    [deps.FilePathsBase.extensions]
    FilePathsBaseMmapExt = "Mmap"
    FilePathsBaseTestExt = "Test"

[[deps.FileWatching]]
uuid = "7b1f6079-737a-58dc-b8bc-7a2ca5c1b5ee"
version = "1.11.0"

[[deps.FillArrays]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "6a70198746448456524cb442b8af316927ff3e1a"
uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
version = "1.13.0"
weakdeps = ["PDMats", "SparseArrays", "Statistics"]

    [deps.FillArrays.extensions]
    FillArraysPDMatsExt = "PDMats"
    FillArraysSparseArraysExt = "SparseArrays"
    FillArraysStatisticsExt = "Statistics"

[[deps.FiniteDiff]]
deps = ["ArrayInterface", "LinearAlgebra", "Setfield"]
git-tree-sha1 = "b10bdafd1647f57ace3885143936749d61638c3b"
uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
version = "2.26.0"

    [deps.FiniteDiff.extensions]
    FiniteDiffBandedMatricesExt = "BandedMatrices"
    FiniteDiffBlockBandedMatricesExt = "BlockBandedMatrices"
    FiniteDiffSparseArraysExt = "SparseArrays"
    FiniteDiffStaticArraysExt = "StaticArrays"

    [deps.FiniteDiff.weakdeps]
    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

[[deps.FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "05882d6995ae5c12bb5f36dd2ed3f61c98cbb172"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.5"

[[deps.Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Zlib_jll"]
git-tree-sha1 = "db16beca600632c95fc8aca29890d83788dd8b23"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.96+0"

[[deps.Format]]
git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc"
uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
version = "1.3.7"

[[deps.Formatting]]
deps = ["Logging", "Printf"]
git-tree-sha1 = "fb409abab2caf118986fc597ba84b50cbaf00b87"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.3"

[[deps.ForwardDiff]]
deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"]
git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad"
uuid = "f6369f11-7733-5829-9624-2563aa707210"
version = "0.10.36"
weakdeps = ["StaticArrays"]

    [deps.ForwardDiff.extensions]
    ForwardDiffStaticArraysExt = "StaticArrays"

[[deps.FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "5c1d8ae0efc6c2e7b1fc502cbe25def8f661b7bc"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.13.2+0"

[[deps.FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1ed150b39aebcc805c26b93a8d0122c940f64ce2"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.14+0"

[[deps.FunctionWrappers]]
git-tree-sha1 = "d62485945ce5ae9c0c48f124a84998d755bae00e"
uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
version = "1.1.3"

[[deps.FunctionWrappersWrappers]]
deps = ["FunctionWrappers"]
git-tree-sha1 = "b104d487b34566608f8b4e1c39fb0b10aa279ff8"
uuid = "77dc65aa-8811-40c2-897b-53d922fa7daf"
version = "0.1.3"

[[deps.Functors]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "64d8e93700c7a3f28f717d265382d52fac9fa1c1"
uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
version = "0.4.12"

[[deps.Future]]
deps = ["Random"]
uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
version = "1.11.0"

[[deps.GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll", "libdecor_jll", "xkbcommon_jll"]
git-tree-sha1 = "532f9126ad901533af1d4f5c198867227a7bb077"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.4.0+1"

[[deps.GLM]]
deps = ["Distributions", "LinearAlgebra", "Printf", "Reexport", "SparseArrays", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns", "StatsModels"]
git-tree-sha1 = "97829cfda0df99ddaeaafb5b370d6cab87b7013e"
uuid = "38e38edf-8417-5370-95a0-9cbb8c7f171a"
version = "1.8.3"

[[deps.GPUArraysCore]]
deps = ["Adapt"]
git-tree-sha1 = "ec632f177c0d990e64d955ccc1b8c04c485a0950"
uuid = "46192b85-c4d5-4398-a991-12ede77f4527"
version = "0.1.6"

[[deps.GR]]
deps = ["Artifacts", "Base64", "DelimitedFiles", "Downloads", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Preferences", "Printf", "Qt6Wayland_jll", "Random", "Serialization", "Sockets", "TOML", "Tar", "Test", "p7zip_jll"]
git-tree-sha1 = "ee28ddcd5517d54e417182fec3886e7412d3926f"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.73.8"

[[deps.GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "FreeType2_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Qt6Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "f31929b9e67066bee48eec8b03c0df47d31a74b3"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.73.8+0"

[[deps.Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[deps.Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE2_jll", "Zlib_jll"]
git-tree-sha1 = "674ff0db93fffcd11a3573986e550d66cd4fd71f"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.80.5+0"

[[deps.Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[deps.Graphs]]
deps = ["ArnoldiMethod", "Compat", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
git-tree-sha1 = "1dc470db8b1131cfc7fb4c115de89fe391b9e780"
uuid = "86223c79-3864-5bf0-83f7-82e725a168b6"
version = "1.12.0"

[[deps.Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[deps.HTTP]]
deps = ["Base64", "CodecZlib", "ConcurrentUtilities", "Dates", "ExceptionUnwrapping", "Logging", "LoggingExtras", "MbedTLS", "NetworkOptions", "OpenSSL", "Random", "SimpleBufferStream", "Sockets", "URIs", "UUIDs"]
git-tree-sha1 = "d1d712be3164d61d1fb98e7ce9bcbc6cc06b45ed"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "1.10.8"

[[deps.HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll"]
git-tree-sha1 = "401e4f3f30f43af2c8478fc008da50096ea5240f"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "8.3.1+0"

[[deps.HybridArrays]]
deps = ["LinearAlgebra", "Requires", "StaticArrays"]
git-tree-sha1 = "6c3e57bc26728b99f470b267a437f0d380eac4fc"
uuid = "1baab800-613f-4b0a-84e4-9cd3431bfbb9"
version = "0.4.16"

[[deps.HypergeometricFunctions]]
deps = ["LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"]
git-tree-sha1 = "7c4195be1649ae622304031ed46a2f4df989f1eb"
uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
version = "0.3.24"

[[deps.Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "179267cfa5e712760cd43dcae385d7ea90cc25a4"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.5"

[[deps.HypertextLiteral]]
deps = ["Tricks"]
git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.5"

[[deps.IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "b6d6bfdd7ce25b0f9b2f6b3dd56b2673a66c8770"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.5"

[[deps.IfElse]]
git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
version = "0.1.1"

[[deps.Indexing]]
git-tree-sha1 = "ce1566720fd6b19ff3411404d4b977acd4814f9f"
uuid = "313cdc1a-70c2-5d6a-ae34-0150d3930a38"
version = "1.1.1"

[[deps.Inflate]]
git-tree-sha1 = "d1b1b796e47d94588b3757fe84fbf65a5ec4a80d"
uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
version = "0.1.5"

[[deps.InitialValues]]
git-tree-sha1 = "4da0f88e9a39111c2fa3add390ab15f3a44f3ca3"
uuid = "22cec73e-a1b8-11e9-2c92-598750a2cf9c"
version = "0.3.1"

[[deps.InlineStrings]]
git-tree-sha1 = "45521d31238e87ee9f9732561bfee12d4eebd52d"
uuid = "842dd82b-1e85-43dc-bf29-5d0ee9dffc48"
version = "1.4.2"

    [deps.InlineStrings.extensions]
    ArrowTypesExt = "ArrowTypes"
    ParsersExt = "Parsers"

    [deps.InlineStrings.weakdeps]
    ArrowTypes = "31f734f8-188a-4ce0-8406-c8a06bd891cd"
    Parsers = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"

[[deps.InplaceOps]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "50b41d59e7164ab6fda65e71049fee9d890731ff"
uuid = "505f98c9-085e-5b2c-8e89-488be7bf1f34"
version = "0.3.0"

[[deps.IntegerMathUtils]]
git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30"
uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
version = "0.1.2"

[[deps.IntelOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl"]
git-tree-sha1 = "10bd689145d2c3b2a9844005d01087cc1194e79e"
uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
version = "2024.2.1+0"

[[deps.InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
version = "1.11.0"

[[deps.Interpolations]]
deps = ["Adapt", "AxisAlgorithms", "ChainRulesCore", "LinearAlgebra", "OffsetArrays", "Random", "Ratios", "Requires", "SharedArrays", "SparseArrays", "StaticArrays", "WoodburyMatrices"]
git-tree-sha1 = "88a101217d7cb38a7b481ccd50d21876e1d1b0e0"
uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
version = "0.15.1"
weakdeps = ["Unitful"]

    [deps.Interpolations.extensions]
    InterpolationsUnitfulExt = "Unitful"

[[deps.IntervalSets]]
git-tree-sha1 = "dba9ddf07f77f60450fe5d2e2beb9854d9a49bd0"
uuid = "8197267c-284f-5f27-9208-e0e47529a953"
version = "0.7.10"
weakdeps = ["Random", "RecipesBase", "Statistics"]

    [deps.IntervalSets.extensions]
    IntervalSetsRandomExt = "Random"
    IntervalSetsRecipesBaseExt = "RecipesBase"
    IntervalSetsStatisticsExt = "Statistics"

[[deps.InverseFunctions]]
git-tree-sha1 = "a779299d77cd080bf77b97535acecd73e1c5e5cb"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.17"
weakdeps = ["Dates", "Test"]

    [deps.InverseFunctions.extensions]
    InverseFunctionsDatesExt = "Dates"
    InverseFunctionsTestExt = "Test"

[[deps.InvertedIndices]]
git-tree-sha1 = "0dc7b50b8d436461be01300fd8cd45aa0274b038"
uuid = "41ab1584-1d38-5bbf-9106-f11c6c58b48f"
version = "1.3.0"

[[deps.IrrationalConstants]]
git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.2.2"

[[deps.IterTools]]
git-tree-sha1 = "42d5f897009e7ff2cf88db414a389e5ed1bdd023"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.10.0"

[[deps.IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[deps.JLFzf]]
deps = ["Pipe", "REPL", "Random", "fzf_jll"]
git-tree-sha1 = "39d64b09147620f5ffbf6b2d3255be3c901bec63"
uuid = "1019f520-868f-41f5-a6de-eb00f4b6a39c"
version = "0.1.8"

[[deps.JLLWrappers]]
deps = ["Artifacts", "Preferences"]
git-tree-sha1 = "be3dc50a92e5a386872a493a10050136d4703f9b"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.6.1"

[[deps.JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "31e996f0a15c7b280ba9f76636b3ff9e2ae58c9a"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.4"

[[deps.JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "25ee0be4d43d0269027024d75a24c24d6c6e590c"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "3.0.4+0"

[[deps.KernelAbstractions]]
deps = ["Adapt", "Atomix", "InteractiveUtils", "MacroTools", "PrecompileTools", "Requires", "StaticArrays", "UUIDs", "UnsafeAtomics", "UnsafeAtomicsLLVM"]
git-tree-sha1 = "04e52f596d0871fa3890170fa79cb15e481e4cd8"
uuid = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
version = "0.9.28"

    [deps.KernelAbstractions.extensions]
    EnzymeExt = "EnzymeCore"
    LinearAlgebraExt = "LinearAlgebra"
    SparseArraysExt = "SparseArrays"

    [deps.KernelAbstractions.weakdeps]
    EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[deps.KernelDensity]]
deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
git-tree-sha1 = "7d703202e65efa1369de1279c162b915e245eed1"
uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
version = "0.6.9"

[[deps.Kronecker]]
deps = ["LinearAlgebra", "NamedDims", "SparseArrays", "StatsBase"]
git-tree-sha1 = "9253429e28cceae6e823bec9ffde12460d79bb38"
uuid = "2c470bb0-bcc8-11e8-3dad-c9649493f05e"
version = "0.5.5"

[[deps.LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "170b660facf5df5de098d866564877e119141cbd"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.2+0"

[[deps.LBFGSB]]
deps = ["L_BFGS_B_jll"]
git-tree-sha1 = "e2e6f53ee20605d0ea2be473480b7480bd5091b5"
uuid = "5be7bae1-8223-5378-bac3-9e7378a2f6e6"
version = "0.4.1"

[[deps.LERC_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "36bdbc52f13a7d1dcb0f3cd694e01677a515655b"
uuid = "88015f11-f218-50d7-93a8-a6af411a945d"
version = "4.0.0+0"

[[deps.LLVM]]
deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Preferences", "Printf", "Requires", "Unicode"]
git-tree-sha1 = "4ad43cb0a4bb5e5b1506e1d1f48646d7e0c80363"
uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
version = "9.1.2"

    [deps.LLVM.extensions]
    BFloat16sExt = "BFloat16s"

    [deps.LLVM.weakdeps]
    BFloat16s = "ab4f0b2a-ad5b-11e8-123f-65d77653426b"

[[deps.LLVMExtra_jll]]
deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "TOML"]
git-tree-sha1 = "05a8bd5a42309a9ec82f700876903abce1017dd3"
uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
version = "0.0.34+0"

[[deps.LLVMOpenMP_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "78211fb6cbc872f77cad3fc0b6cf647d923f4929"
uuid = "1d63c593-3942-5779-bab2-d838dc0a180e"
version = "18.1.7+0"

[[deps.LRUCache]]
git-tree-sha1 = "b3cc6698599b10e652832c2f23db3cab99d51b59"
uuid = "8ac3fa9e-de4c-5943-b1dc-09c6b5f20637"
version = "1.6.1"
weakdeps = ["Serialization"]

    [deps.LRUCache.extensions]
    SerializationExt = ["Serialization"]

[[deps.LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "854a9c268c43b77b0a27f22d7fab8d33cdb3a731"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.2+1"

[[deps.L_BFGS_B_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "77feda930ed3f04b2b0fbb5bea89e69d3677c6b0"
uuid = "81d17ec3-03a1-5e46-b53e-bddc35a13473"
version = "3.0.1+0"

[[deps.LaTeXStrings]]
git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.1"

[[deps.Latexify]]
deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
git-tree-sha1 = "ce5f5621cac23a86011836badfedf664a612cee4"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.16.5"

    [deps.Latexify.extensions]
    DataFramesExt = "DataFrames"
    SparseArraysExt = "SparseArrays"
    SymEngineExt = "SymEngine"

    [deps.Latexify.weakdeps]
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"

[[deps.LazyArtifacts]]
deps = ["Artifacts", "Pkg"]
uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
version = "1.11.0"

[[deps.LeftChildRightSiblingTrees]]
deps = ["AbstractTrees"]
git-tree-sha1 = "fb6803dafae4a5d62ea5cab204b1e657d9737e7f"
uuid = "1d6d02ad-be62-4b6b-8a6d-2f90e265016e"
version = "0.2.0"

[[deps.LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
version = "0.6.4"

[[deps.LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
version = "8.6.0+0"

[[deps.LibGit2]]
deps = ["Base64", "LibGit2_jll", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
version = "1.11.0"

[[deps.LibGit2_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll"]
uuid = "e37daf67-58a4-590a-8e99-b0245dd2ffc5"
version = "1.7.2+0"

[[deps.LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
version = "1.11.0+1"

[[deps.Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
version = "1.11.0"

[[deps.Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[deps.Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll"]
git-tree-sha1 = "9fd170c4bbfd8b935fdc5f8b7aa33532c991a673"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.11+0"

[[deps.Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "6f73d1dd803986947b2c750138528a999a6c7733"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.6.0+0"

[[deps.Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "fbb1f2bef882392312feb1ede3615ddc1e9b99ed"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.49.0+0"

[[deps.Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "f9557a255370125b405568f9767d6d195822a175"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.17.0+0"

[[deps.Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "0c4f9c4f1a50d8f35048fa0532dabbadf702f81e"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.40.1+0"

[[deps.Libtask]]
deps = ["FunctionWrappers", "LRUCache", "LinearAlgebra", "Statistics"]
git-tree-sha1 = "ed1f362b3fd13f00b65e61d98669c652c17663ab"
uuid = "6f1fad26-d15e-5dc8-ae53-837a1d7b8c9f"
version = "0.8.7"

[[deps.Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "LERC_jll", "Libdl", "XZ_jll", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "b404131d06f7886402758c9ce2214b636eb4d54a"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.7.0+0"

[[deps.Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "5ee6203157c120d79034c748a2acba45b82b8807"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.40.1+0"

[[deps.LineSearches]]
deps = ["LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "Printf"]
git-tree-sha1 = "e4c3be53733db1051cc15ecf573b1042b3a712a1"
uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
version = "7.3.0"

[[deps.LinearAlgebra]]
deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
version = "1.11.0"

[[deps.LinearMaps]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "ee79c3208e55786de58f8dcccca098ced79f743f"
uuid = "7a12625a-238d-50fd-b39a-03d52299707e"
version = "3.11.3"
weakdeps = ["ChainRulesCore", "SparseArrays", "Statistics"]

    [deps.LinearMaps.extensions]
    LinearMapsChainRulesCoreExt = "ChainRulesCore"
    LinearMapsSparseArraysExt = "SparseArrays"
    LinearMapsStatisticsExt = "Statistics"

[[deps.LogDensityProblems]]
deps = ["ArgCheck", "DocStringExtensions", "Random"]
git-tree-sha1 = "4e0128c1590d23a50dcdb106c7e2dbca99df85c0"
uuid = "6fdf6af0-433a-55f7-b3ed-c6c6e0b8df7c"
version = "2.1.2"

[[deps.LogDensityProblemsAD]]
deps = ["DocStringExtensions", "LogDensityProblems"]
git-tree-sha1 = "3092250f021aca6d3e24036019cbb24c0c5d89df"
uuid = "996a588d-648d-4e1f-a8f0-a84b347e47b1"
version = "1.11.0"

    [deps.LogDensityProblemsAD.extensions]
    LogDensityProblemsADADTypesExt = "ADTypes"
    LogDensityProblemsADEnzymeExt = "Enzyme"
    LogDensityProblemsADFiniteDifferencesExt = "FiniteDifferences"
    LogDensityProblemsADForwardDiffBenchmarkToolsExt = ["BenchmarkTools", "ForwardDiff"]
    LogDensityProblemsADForwardDiffExt = "ForwardDiff"
    LogDensityProblemsADReverseDiffExt = "ReverseDiff"
    LogDensityProblemsADTrackerExt = "Tracker"
    LogDensityProblemsADZygoteExt = "Zygote"

    [deps.LogDensityProblemsAD.weakdeps]
    ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
    BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
    FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.LogExpFunctions]]
deps = ["DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "a2d09619db4e765091ee5c6ffe8872849de0feea"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.28"
weakdeps = ["ChainRulesCore", "ChangesOfVariables", "InverseFunctions"]

    [deps.LogExpFunctions.extensions]
    LogExpFunctionsChainRulesCoreExt = "ChainRulesCore"
    LogExpFunctionsChangesOfVariablesExt = "ChangesOfVariables"
    LogExpFunctionsInverseFunctionsExt = "InverseFunctions"

[[deps.Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
version = "1.11.0"

[[deps.LoggingExtras]]
deps = ["Dates", "Logging"]
git-tree-sha1 = "c1dd6d7978c12545b4179fb6153b9250c96b0075"
uuid = "e6f89c97-d47a-5376-807f-9c37f3926c36"
version = "1.0.3"

[[deps.MCMCChains]]
deps = ["AbstractMCMC", "AxisArrays", "Dates", "Distributions", "IteratorInterfaceExtensions", "KernelDensity", "LinearAlgebra", "MCMCDiagnosticTools", "MLJModelInterface", "NaturalSort", "OrderedCollections", "PrettyTables", "Random", "RecipesBase", "Statistics", "StatsBase", "StatsFuns", "TableTraits", "Tables"]
git-tree-sha1 = "d28056379864318172ff4b7958710cfddd709339"
uuid = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
version = "6.0.6"

[[deps.MCMCDiagnosticTools]]
deps = ["AbstractFFTs", "DataAPI", "DataStructures", "Distributions", "LinearAlgebra", "MLJModelInterface", "Random", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Tables"]
git-tree-sha1 = "8ba8b1840d3ab5b38e7c71c23c3193bb5cbc02b5"
uuid = "be115224-59cd-429b-ad48-344e309966f0"
version = "0.3.10"

[[deps.MIMEs]]
git-tree-sha1 = "65f28ad4b594aebe22157d6fac869786a255b7eb"
uuid = "6c6e2e6c-3030-632d-7369-2d6c69616d65"
version = "0.1.4"

[[deps.MKL_jll]]
deps = ["Artifacts", "IntelOpenMP_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "oneTBB_jll"]
git-tree-sha1 = "f046ccd0c6db2832a9f639e2c669c6fe867e5f4f"
uuid = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
version = "2024.2.0+0"

[[deps.MLJModelInterface]]
deps = ["Random", "ScientificTypesBase", "StatisticalTraits"]
git-tree-sha1 = "ceaff6618408d0e412619321ae43b33b40c1a733"
uuid = "e80e1ace-859a-464e-9ed9-23947d8ae3ea"
version = "1.11.0"

[[deps.MLStyle]]
git-tree-sha1 = "bc38dff0548128765760c79eb7388a4b37fae2c8"
uuid = "d8e11817-5142-5d16-987a-aa16d5891078"
version = "0.4.17"

[[deps.MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.13"

[[deps.ManifoldDiff]]
deps = ["LinearAlgebra", "ManifoldsBase", "Markdown", "Random", "Requires"]
git-tree-sha1 = "62fccd67f9fb83526bff40a1432f63464eb6d282"
uuid = "af67fdf4-a580-4b9f-bbec-742ef357defd"
version = "0.3.12"

    [deps.ManifoldDiff.extensions]
    ManifoldDiffFiniteDiffExt = "FiniteDiff"
    ManifoldDiffFiniteDifferencesExt = "FiniteDifferences"
    ManifoldDiffForwardDiffExt = "ForwardDiff"
    ManifoldDiffReverseDiffExt = "ReverseDiff"
    ManifoldDiffZygoteExt = "Zygote"

    [deps.ManifoldDiff.weakdeps]
    FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
    FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.Manifolds]]
deps = ["Distributions", "Einsum", "Graphs", "HybridArrays", "Kronecker", "LinearAlgebra", "ManifoldDiff", "ManifoldsBase", "Markdown", "MatrixEquations", "Quaternions", "Random", "RecursiveArrayTools", "Requires", "SimpleWeightedGraphs", "SpecialFunctions", "StaticArrays", "Statistics", "StatsBase"]
git-tree-sha1 = "58eb09899273a3ed17aae1f56435f440669b810c"
uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
version = "0.9.20"

    [deps.Manifolds.extensions]
    ManifoldsBoundaryValueDiffEqExt = "BoundaryValueDiffEq"
    ManifoldsNLsolveExt = "NLsolve"
    ManifoldsOrdinaryDiffEqDiffEqCallbacksExt = ["DiffEqCallbacks", "OrdinaryDiffEq"]
    ManifoldsOrdinaryDiffEqExt = "OrdinaryDiffEq"
    ManifoldsRecipesBaseExt = ["Colors", "RecipesBase"]
    ManifoldsTestExt = "Test"

    [deps.Manifolds.weakdeps]
    BoundaryValueDiffEq = "764a87c0-6b3e-53db-9096-fe964310641d"
    Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
    DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
    NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
    OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
    RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[deps.ManifoldsBase]]
deps = ["LinearAlgebra", "Markdown", "Printf", "Random", "Requires"]
git-tree-sha1 = "4259c5f29dbe9d7441ec0f5ce31c2a6895285495"
uuid = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
version = "0.15.17"
weakdeps = ["Plots", "Quaternions", "RecursiveArrayTools", "Statistics"]

    [deps.ManifoldsBase.extensions]
    ManifoldsBasePlotsExt = "Plots"
    ManifoldsBaseQuaternionsExt = "Quaternions"
    ManifoldsBaseRecursiveArrayToolsExt = "RecursiveArrayTools"
    ManifoldsBaseStatisticsExt = "Statistics"

[[deps.MappedArrays]]
git-tree-sha1 = "2dab0221fe2b0f2cb6754eaa743cc266339f527e"
uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
version = "0.4.2"

[[deps.Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
version = "1.11.0"

[[deps.MatrixEquations]]
deps = ["LinearAlgebra", "LinearMaps"]
git-tree-sha1 = "f765b4eda3ea9be8e644b9127809ca5151f3d9ea"
uuid = "99c1a7ee-ab34-5fd5-8076-27c950a045f4"
version = "2.4.2"

[[deps.MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "MozillaCACerts_jll", "NetworkOptions", "Random", "Sockets"]
git-tree-sha1 = "c067a280ddc25f196b5e7df3877c6b226d390aaf"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.1.9"

[[deps.MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
version = "2.28.6+0"

[[deps.Measures]]
git-tree-sha1 = "c13304c81eec1ed3af7fc20e75fb6b26092a1102"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.2"

[[deps.MicroCollections]]
deps = ["Accessors", "BangBang", "InitialValues"]
git-tree-sha1 = "44d32db644e84c75dab479f1bc15ee76a1a3618f"
uuid = "128add7d-3638-4c79-886c-908ea0c25c34"
version = "0.2.0"

[[deps.Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "ec4f7fbeab05d7747bdf98eb74d130a2a2ed298d"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.2.0"

[[deps.Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"
version = "1.11.0"

[[deps.Mocking]]
deps = ["Compat", "ExprTools"]
git-tree-sha1 = "2c140d60d7cb82badf06d8783800d0bcd1a7daa2"
uuid = "78c3b35d-d492-501b-9361-3d52fe80e533"
version = "0.8.1"

[[deps.MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
version = "2023.12.12"

[[deps.MultivariatePolynomials]]
deps = ["ChainRulesCore", "DataStructures", "LinearAlgebra", "MutableArithmetics"]
git-tree-sha1 = "8d39779e29f80aa6c071e7ac17101c6e31f075d7"
uuid = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
version = "0.5.7"

[[deps.MultivariateStats]]
deps = ["Arpack", "Distributions", "LinearAlgebra", "SparseArrays", "Statistics", "StatsAPI", "StatsBase"]
git-tree-sha1 = "816620e3aac93e5b5359e4fdaf23ca4525b00ddf"
uuid = "6f286f6a-111f-5878-ab1e-185364afe411"
version = "0.10.3"

[[deps.MutableArithmetics]]
deps = ["LinearAlgebra", "SparseArrays", "Test"]
git-tree-sha1 = "90077f1e79de8c9c7c8a90644494411111f4e07b"
uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
version = "1.5.2"

[[deps.NLSolversBase]]
deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
git-tree-sha1 = "a0b464d183da839699f4c79e7606d9d186ec172c"
uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
version = "7.8.3"

[[deps.NNlib]]
deps = ["Adapt", "Atomix", "ChainRulesCore", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "da09a1e112fd75f9af2a5229323f01b56ec96a4c"
uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
version = "0.9.24"

    [deps.NNlib.extensions]
    NNlibAMDGPUExt = "AMDGPU"
    NNlibCUDACUDNNExt = ["CUDA", "cuDNN"]
    NNlibCUDAExt = "CUDA"
    NNlibEnzymeCoreExt = "EnzymeCore"
    NNlibFFTWExt = "FFTW"
    NNlibForwardDiffExt = "ForwardDiff"

    [deps.NNlib.weakdeps]
    AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e"
    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
    EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
    FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    cuDNN = "02a925ec-e4fe-4b08-9a7e-0d78e3d38ccd"

[[deps.NaNMath]]
deps = ["OpenLibm_jll"]
git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "1.0.2"

[[deps.NamedArrays]]
deps = ["Combinatorics", "DataStructures", "DelimitedFiles", "InvertedIndices", "LinearAlgebra", "Random", "Requires", "SparseArrays", "Statistics"]
git-tree-sha1 = "58e317b3b956b8aaddfd33ff4c3e33199cd8efce"
uuid = "86f7a689-2022-50b4-a561-43c23ac3c673"
version = "0.10.3"

[[deps.NamedDims]]
deps = ["LinearAlgebra", "Pkg", "Statistics"]
git-tree-sha1 = "90178dc801073728b8b2d0d8677d10909feb94d8"
uuid = "356022a1-0364-5f58-8944-0da4b18d706f"
version = "1.2.2"

    [deps.NamedDims.extensions]
    AbstractFFTsExt = "AbstractFFTs"
    ChainRulesCoreExt = "ChainRulesCore"
    CovarianceEstimationExt = "CovarianceEstimation"
    TrackerExt = "Tracker"

    [deps.NamedDims.weakdeps]
    AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    CovarianceEstimation = "587fd27a-f159-11e8-2dae-1979310e6154"
    Requires = "ae029012-a4dd-5104-9daa-d747884805df"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"

[[deps.NaturalSort]]
git-tree-sha1 = "eda490d06b9f7c00752ee81cfa451efe55521e21"
uuid = "c020b1a1-e9b0-503a-9c33-f039bfc54a85"
version = "1.0.0"

[[deps.NearestNeighbors]]
deps = ["Distances", "StaticArrays"]
git-tree-sha1 = "3cebfc94a0754cc329ebc3bab1e6c89621e791ad"
uuid = "b8a86587-4115-5ab1-83bc-aa920d37bbce"
version = "0.4.20"

[[deps.NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
version = "1.2.0"

[[deps.Observables]]
git-tree-sha1 = "7438a59546cf62428fc9d1bc94729146d37a7225"
uuid = "510215fc-4207-5dde-b226-833fc4488ee2"
version = "0.5.5"

[[deps.OffsetArrays]]
git-tree-sha1 = "1a27764e945a152f7ca7efa04de513d473e9542e"
uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
version = "1.14.1"
weakdeps = ["Adapt"]

    [deps.OffsetArrays.extensions]
    OffsetArraysAdaptExt = "Adapt"

[[deps.Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "887579a3eb005446d514ab7aeac5d1d027658b8f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+1"

[[deps.OpenBLAS_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
version = "0.3.27+1"

[[deps.OpenLibm_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
version = "0.8.1+2"

[[deps.OpenSSL]]
deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]
git-tree-sha1 = "38cb508d080d21dc1128f7fb04f20387ed4c0af4"
uuid = "4d8831e6-92b7-49fb-bdf8-b643e874388c"
version = "1.4.3"

[[deps.OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7493f61f55a6cce7325f197443aa80d32554ba10"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "3.0.15+1"

[[deps.OpenSpecFun_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
version = "0.5.5+0"

[[deps.Optim]]
deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
git-tree-sha1 = "d9b79c4eed437421ac4285148fcadf42e0700e89"
uuid = "429524aa-4258-5aef-a3af-852621145aeb"
version = "1.9.4"

    [deps.Optim.extensions]
    OptimMOIExt = "MathOptInterface"

    [deps.Optim.weakdeps]
    MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"

[[deps.Optimisers]]
deps = ["ChainRulesCore", "Functors", "LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "6572fe0c5b74431aaeb0b18a4aa5ef03c84678be"
uuid = "3bd65402-5787-11e9-1adc-39752487f4e2"
version = "0.3.3"

[[deps.Optimization]]
deps = ["ADTypes", "ArrayInterface", "ConsoleProgressMonitor", "DocStringExtensions", "LBFGSB", "LinearAlgebra", "Logging", "LoggingExtras", "OptimizationBase", "Printf", "ProgressLogging", "Reexport", "SciMLBase", "SparseArrays", "TerminalLoggers"]
git-tree-sha1 = "0b2a631276dc92ab147535689fa43f1e22a657b8"
uuid = "7f7a1694-90dd-40f0-9382-eb1efda571ba"
version = "3.28.0"

[[deps.OptimizationBase]]
deps = ["ADTypes", "ArrayInterface", "DocStringExtensions", "LinearAlgebra", "PDMats", "Reexport", "Requires", "SciMLBase", "SparseArrays", "SymbolicAnalysis", "SymbolicIndexingInterface", "Symbolics"]
git-tree-sha1 = "3e5e5e8cbe572200dcd94a6084a63ca68fe76279"
uuid = "bca83a33-5cc9-4baa-983d-23429ab6bcbb"
version = "1.5.0"

    [deps.OptimizationBase.extensions]
    OptimizationEnzymeExt = "Enzyme"
    OptimizationFiniteDiffExt = "FiniteDiff"
    OptimizationForwardDiffExt = "ForwardDiff"
    OptimizationMTKExt = "ModelingToolkit"
    OptimizationReverseDiffExt = "ReverseDiff"
    OptimizationSparseDiffExt = ["SparseDiffTools", "ReverseDiff"]
    OptimizationTrackerExt = "Tracker"
    OptimizationZygoteExt = "Zygote"

    [deps.OptimizationBase.weakdeps]
    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
    FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.OptimizationOptimJL]]
deps = ["Optim", "Optimization", "Reexport", "SparseArrays"]
git-tree-sha1 = "43870d726f883a47d158beebb1fc3c9fab1da9d6"
uuid = "36348300-93cb-4f02-beb5-3c3902f8871e"
version = "0.3.2"

[[deps.Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6703a85cb3781bd5909d48730a67205f3f31a575"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.3+0"

[[deps.OrderedCollections]]
git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.6.3"

[[deps.PCRE2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "efcefdf7-47ab-520b-bdef-62a2eaa19f15"
version = "10.42.0+1"

[[deps.PDMats]]
deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "949347156c25054de2db3b166c52ac4728cbad65"
uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
version = "0.11.31"

[[deps.Pango_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "FriBidi_jll", "Glib_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e127b609fb9ecba6f201ba7ab753d5a605d53801"
uuid = "36c8627f-9965-5494-a995-c6b170f724f3"
version = "1.54.1+0"

[[deps.Parameters]]
deps = ["OrderedCollections", "UnPack"]
git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
version = "0.12.3"

[[deps.Parsers]]
deps = ["Dates", "PrecompileTools", "UUIDs"]
git-tree-sha1 = "8489905bcdbcfac64d1daa51ca07c0d8f0283821"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.8.1"

[[deps.Pipe]]
git-tree-sha1 = "6842804e7867b115ca9de748a0cf6b364523c16d"
uuid = "b98c9c47-44ae-5843-9183-064241ee97a0"
version = "1.3.0"

[[deps.Pixman_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "LLVMOpenMP_jll", "Libdl"]
git-tree-sha1 = "35621f10a7531bc8fa58f74610b1bfb70a3cfc6b"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.43.4+0"

[[deps.Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "Random", "SHA", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
version = "1.11.0"
weakdeps = ["REPL"]

    [deps.Pkg.extensions]
    REPLExt = "REPL"

[[deps.PlotThemes]]
deps = ["PlotUtils", "Statistics"]
git-tree-sha1 = "6e55c6841ce3411ccb3457ee52fc48cb698d6fb0"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "3.2.0"

[[deps.PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "PrecompileTools", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "7b1a9df27f072ac4c9c7cbe5efb198489258d1f5"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.4.1"

[[deps.Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "JLFzf", "JSON", "LaTeXStrings", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "Pkg", "PlotThemes", "PlotUtils", "PrecompileTools", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "RelocatableFolders", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "TOML", "UUIDs", "UnicodeFun", "UnitfulLatexify", "Unzip"]
git-tree-sha1 = "45470145863035bb124ca51b320ed35d071cc6c2"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.40.8"

    [deps.Plots.extensions]
    FileIOExt = "FileIO"
    GeometryBasicsExt = "GeometryBasics"
    IJuliaExt = "IJulia"
    ImageInTerminalExt = "ImageInTerminal"
    UnitfulExt = "Unitful"

    [deps.Plots.weakdeps]
    FileIO = "5789e2e9-d7fb-5bc7-8068-2c6fae9b9549"
    GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
    IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
    ImageInTerminal = "d8c32880-2388-543b-8c61-d9f865259254"
    Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"

[[deps.PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "ColorTypes", "Dates", "FixedPointNumbers", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "MIMEs", "Markdown", "Random", "Reexport", "URIs", "UUIDs"]
git-tree-sha1 = "eba4810d5e6a01f612b948c9fa94f905b49087b0"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.60"

[[deps.Polynomials]]
deps = ["LinearAlgebra", "RecipesBase", "Requires", "Setfield", "SparseArrays"]
git-tree-sha1 = "1a9cfb2dc2c2f1bd63f1906d72af39a79b49b736"
uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
version = "4.0.11"

    [deps.Polynomials.extensions]
    PolynomialsChainRulesCoreExt = "ChainRulesCore"
    PolynomialsFFTWExt = "FFTW"
    PolynomialsMakieCoreExt = "MakieCore"
    PolynomialsMutableArithmeticsExt = "MutableArithmetics"

    [deps.Polynomials.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
    MakieCore = "20f20a25-4f0e-4fdf-b5d1-57303727442b"
    MutableArithmetics = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"

[[deps.PooledArrays]]
deps = ["DataAPI", "Future"]
git-tree-sha1 = "36d8b4b899628fb92c2749eb488d884a926614d3"
uuid = "2dfb63ee-cc39-5dd5-95bd-886bf059d720"
version = "1.4.3"

[[deps.PositiveFactorizations]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
version = "0.2.4"

[[deps.PrecompileTools]]
deps = ["Preferences"]
git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
uuid = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
version = "1.2.1"

[[deps.Preferences]]
deps = ["TOML"]
git-tree-sha1 = "9306f6085165d270f7e3db02af26a400d580f5c6"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.4.3"

[[deps.PrettyTables]]
deps = ["Crayons", "Formatting", "Markdown", "Reexport", "Tables"]
git-tree-sha1 = "dfb54c4e414caa595a1f2ed759b160f5a3ddcba5"
uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
version = "1.3.1"

[[deps.Primes]]
deps = ["IntegerMathUtils"]
git-tree-sha1 = "cb420f77dc474d23ee47ca8d14c90810cafe69e7"
uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
version = "0.5.6"

[[deps.Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
version = "1.11.0"

[[deps.ProgressLogging]]
deps = ["Logging", "SHA", "UUIDs"]
git-tree-sha1 = "80d919dee55b9c50e8d9e2da5eeafff3fe58b539"
uuid = "33c8b6b6-d38a-422a-b730-caa89a2f386c"
version = "0.1.4"

[[deps.ProgressMeter]]
deps = ["Distributed", "Printf"]
git-tree-sha1 = "8f6bc219586aef8baf0ff9a5fe16ee9c70cb65e4"
uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
version = "1.10.2"

[[deps.PtrArrays]]
git-tree-sha1 = "77a42d78b6a92df47ab37e177b2deac405e1c88f"
uuid = "43287f4e-b6f4-7ad1-bb20-aadabca52c3d"
version = "1.2.1"

[[deps.Qt6Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Vulkan_Loader_jll", "Xorg_libSM_jll", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_cursor_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "libinput_jll", "xkbcommon_jll"]
git-tree-sha1 = "492601870742dcd38f233b23c3ec629628c1d724"
uuid = "c0090381-4147-56d7-9ebc-da0b1113ec56"
version = "6.7.1+1"

[[deps.Qt6Declarative_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6ShaderTools_jll"]
git-tree-sha1 = "e5dd466bf2569fe08c91a2cc29c1003f4797ac3b"
uuid = "629bc702-f1f5-5709-abd5-49b8460ea067"
version = "6.7.1+2"

[[deps.Qt6ShaderTools_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll"]
git-tree-sha1 = "1a180aeced866700d4bebc3120ea1451201f16bc"
uuid = "ce943373-25bb-56aa-8eca-768745ed7b5a"
version = "6.7.1+1"

[[deps.Qt6Wayland_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Qt6Base_jll", "Qt6Declarative_jll"]
git-tree-sha1 = "729927532d48cf79f49070341e1d918a65aba6b0"
uuid = "e99dba38-086e-5de3-a5b1-6e4c66e897c3"
version = "6.7.1+1"

[[deps.QuadGK]]
deps = ["DataStructures", "LinearAlgebra"]
git-tree-sha1 = "cda3b045cf9ef07a08ad46731f5a3165e56cf3da"
uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
version = "2.11.1"

    [deps.QuadGK.extensions]
    QuadGKEnzymeExt = "Enzyme"

    [deps.QuadGK.weakdeps]
    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"

[[deps.Quaternions]]
deps = ["LinearAlgebra", "Random", "RealDot"]
git-tree-sha1 = "994cc27cdacca10e68feb291673ec3a76aa2fae9"
uuid = "94ee1d12-ae83-5a48-8b1c-48b8ff168ae0"
version = "0.7.6"

[[deps.RData]]
deps = ["CategoricalArrays", "CodecZlib", "DataFrames", "Dates", "FileIO", "Requires", "TimeZones", "Unicode"]
git-tree-sha1 = "19e47a495dfb7240eb44dc6971d660f7e4244a72"
uuid = "df47a6cb-8c03-5eed-afd8-b6050d6c41da"
version = "0.8.3"

[[deps.RDatasets]]
deps = ["CSV", "CodecZlib", "DataFrames", "FileIO", "Printf", "RData", "Reexport"]
git-tree-sha1 = "2720e6f6afb3e562ccb70a6b62f8f308ff810333"
uuid = "ce6b1742-4840-55fa-b093-852dadbb1d8b"
version = "0.7.7"

[[deps.REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "StyledStrings", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
version = "1.11.0"

[[deps.Random]]
deps = ["SHA"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
version = "1.11.0"

[[deps.Random123]]
deps = ["Random", "RandomNumbers"]
git-tree-sha1 = "4743b43e5a9c4a2ede372de7061eed81795b12e7"
uuid = "74087812-796a-5b5d-8853-05524746bad3"
version = "1.7.0"

[[deps.RandomNumbers]]
deps = ["Random"]
git-tree-sha1 = "c6ec94d2aaba1ab2ff983052cf6a606ca5985902"
uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
version = "1.6.0"

[[deps.RangeArrays]]
git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
version = "0.3.2"

[[deps.Ratios]]
deps = ["Requires"]
git-tree-sha1 = "1342a47bf3260ee108163042310d26f2be5ec90b"
uuid = "c84ed2f1-dad5-54f0-aa8e-dbefe2724439"
version = "0.4.5"
weakdeps = ["FixedPointNumbers"]

    [deps.Ratios.extensions]
    RatiosFixedPointNumbersExt = "FixedPointNumbers"

[[deps.RealDot]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "9f0a1b71baaf7650f4fa8a1d168c7fb6ee41f0c9"
uuid = "c1ae055f-0cd5-4b69-90a6-9a35b1a98df9"
version = "0.1.0"

[[deps.RecipesBase]]
deps = ["PrecompileTools"]
git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.3.4"

[[deps.RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "PrecompileTools", "RecipesBase"]
git-tree-sha1 = "45cf9fd0ca5839d06ef333c8201714e888486342"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.6.12"

[[deps.RecursiveArrayTools]]
deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "IteratorInterfaceExtensions", "LinearAlgebra", "RecipesBase", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
git-tree-sha1 = "b034171b93aebc81b3e1890a036d13a9c4a9e3e0"
uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
version = "3.27.0"

    [deps.RecursiveArrayTools.extensions]
    RecursiveArrayToolsFastBroadcastExt = "FastBroadcast"
    RecursiveArrayToolsForwardDiffExt = "ForwardDiff"
    RecursiveArrayToolsMeasurementsExt = "Measurements"
    RecursiveArrayToolsMonteCarloMeasurementsExt = "MonteCarloMeasurements"
    RecursiveArrayToolsReverseDiffExt = ["ReverseDiff", "Zygote"]
    RecursiveArrayToolsSparseArraysExt = ["SparseArrays"]
    RecursiveArrayToolsTrackerExt = "Tracker"
    RecursiveArrayToolsZygoteExt = "Zygote"

    [deps.RecursiveArrayTools.weakdeps]
    FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
    MonteCarloMeasurements = "0987c9cc-fe09-11e8-30f0-b96dd679fdca"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[deps.RelocatableFolders]]
deps = ["SHA", "Scratch"]
git-tree-sha1 = "ffdaf70d81cf6ff22c2b6e733c900c3321cab864"
uuid = "05181044-ff0b-4ac5-8273-598c1e38db00"
version = "1.0.1"

[[deps.Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "838a3a4188e2ded87a4f9f184b4b0d78a1e91cb7"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.3.0"

[[deps.Rmath]]
deps = ["Random", "Rmath_jll"]
git-tree-sha1 = "852bd0f55565a9e973fcfee83a84413270224dc4"
uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
version = "0.8.0"

[[deps.Rmath_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "58cdd8fb2201a6267e1db87ff148dd6c1dbd8ad8"
uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
version = "0.5.1+0"

[[deps.Roots]]
deps = ["Accessors", "CommonSolve", "Printf"]
git-tree-sha1 = "3a7c7e5c3f015415637f5debdf8a674aa2c979c4"
uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
version = "2.2.1"

    [deps.Roots.extensions]
    RootsChainRulesCoreExt = "ChainRulesCore"
    RootsForwardDiffExt = "ForwardDiff"
    RootsIntervalRootFindingExt = "IntervalRootFinding"
    RootsSymPyExt = "SymPy"
    RootsSymPyPythonCallExt = "SymPyPythonCall"

    [deps.Roots.weakdeps]
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    IntervalRootFinding = "d2bf35a9-74e0-55ec-b149-d360ff49b807"
    SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
    SymPyPythonCall = "bc8888f7-b21e-4b7c-a06a-5d9c9496438c"

[[deps.RuntimeGeneratedFunctions]]
deps = ["ExprTools", "SHA", "Serialization"]
git-tree-sha1 = "04c968137612c4a5629fa531334bb81ad5680f00"
uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
version = "0.5.13"

[[deps.SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
version = "0.7.0"

[[deps.SSMProblems]]
deps = ["AbstractMCMC"]
git-tree-sha1 = "f640e4e8343c9d5f470e2f6ca6ce79f708ab6376"
uuid = "26aad666-b158-4e64-9d35-0e672562fa48"
version = "0.1.1"

[[deps.SciMLBase]]
deps = ["ADTypes", "Accessors", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "Expronicon", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
git-tree-sha1 = "50ed64cd5ad79b0bef71fdb6a11d10c3448bfef0"
uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
version = "2.56.1"

    [deps.SciMLBase.extensions]
    SciMLBaseChainRulesCoreExt = "ChainRulesCore"
    SciMLBaseMakieExt = "Makie"
    SciMLBasePartialFunctionsExt = "PartialFunctions"
    SciMLBasePyCallExt = "PyCall"
    SciMLBasePythonCallExt = "PythonCall"
    SciMLBaseRCallExt = "RCall"
    SciMLBaseZygoteExt = "Zygote"

    [deps.SciMLBase.weakdeps]
    ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
    PartialFunctions = "570af359-4316-4cb7-8c74-252c00c2016b"
    PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
    PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d"
    RCall = "6f49c342-dc21-5d91-9882-a32aef131414"
    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

[[deps.SciMLOperators]]
deps = ["Accessors", "ArrayInterface", "DocStringExtensions", "LinearAlgebra", "MacroTools"]
git-tree-sha1 = "e39c5f217f9aca640c8e27ab21acf557a3967db5"
uuid = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
version = "0.3.10"
weakdeps = ["SparseArrays", "StaticArraysCore"]

    [deps.SciMLOperators.extensions]
    SciMLOperatorsSparseArraysExt = "SparseArrays"
    SciMLOperatorsStaticArraysCoreExt = "StaticArraysCore"

[[deps.SciMLStructures]]
deps = ["ArrayInterface"]
git-tree-sha1 = "25514a6f200219cd1073e4ff23a6324e4a7efe64"
uuid = "53ae85a6-f571-4167-b2af-e1d143709226"
version = "1.5.0"

[[deps.ScientificTypesBase]]
git-tree-sha1 = "a8e18eb383b5ecf1b5e6fc237eb39255044fd92b"
uuid = "30f210dd-8aff-4c5f-94ba-8e64358c1161"
version = "3.0.0"

[[deps.Scratch]]
deps = ["Dates"]
git-tree-sha1 = "3bac05bc7e74a75fd9cba4295cde4045d9fe2386"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.2.1"

[[deps.SentinelArrays]]
deps = ["Dates", "Random"]
git-tree-sha1 = "ff11acffdb082493657550959d4feb4b6149e73a"
uuid = "91c51154-3ec4-41a3-a24f-3f23e20d615c"
version = "1.4.5"

[[deps.Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
version = "1.11.0"

[[deps.Setfield]]
deps = ["ConstructionBase", "Future", "MacroTools", "StaticArraysCore"]
git-tree-sha1 = "e2cc6d8c88613c05e1defb55170bf5ff211fbeac"
uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
version = "1.1.1"

[[deps.SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
version = "1.11.0"

[[deps.ShiftedArrays]]
git-tree-sha1 = "503688b59397b3307443af35cd953a13e8005c16"
uuid = "1277b4bf-5013-50f5-be3d-901d8477a67a"
version = "2.0.0"

[[deps.Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[deps.SimpleBufferStream]]
git-tree-sha1 = "f305871d2f381d21527c770d4788c06c097c9bc1"
uuid = "777ac1f9-54b0-4bf8-805c-2214025038e7"
version = "1.2.0"

[[deps.SimpleTraits]]
deps = ["InteractiveUtils", "MacroTools"]
git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
version = "0.9.4"

[[deps.SimpleUnPack]]
git-tree-sha1 = "58e6353e72cde29b90a69527e56df1b5c3d8c437"
uuid = "ce78b400-467f-4804-87d8-8f486da07d0a"
version = "1.1.0"

[[deps.SimpleWeightedGraphs]]
deps = ["Graphs", "LinearAlgebra", "Markdown", "SparseArrays"]
git-tree-sha1 = "4b33e0e081a825dbfaf314decf58fa47e53d6acb"
uuid = "47aef6b3-ad0c-573a-a1e2-d07658019622"
version = "1.4.0"

[[deps.Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
version = "1.11.0"

[[deps.SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "66e0a8e672a0bdfca2c3f5937efb8538b9ddc085"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.2.1"

[[deps.SparseArrays]]
deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
version = "1.11.0"

[[deps.SparseInverseSubset]]
deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
git-tree-sha1 = "52962839426b75b3021296f7df242e40ecfc0852"
uuid = "dc90abb0-5640-4711-901d-7e5b23a2fada"
version = "0.1.2"

[[deps.SpecialFunctions]]
deps = ["IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
git-tree-sha1 = "2f5d4697f21388cbe1ff299430dd169ef97d7e14"
uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
version = "2.4.0"
weakdeps = ["ChainRulesCore"]

    [deps.SpecialFunctions.extensions]
    SpecialFunctionsChainRulesCoreExt = "ChainRulesCore"

[[deps.SplittablesBase]]
deps = ["Setfield", "Test"]
git-tree-sha1 = "e08a62abc517eb79667d0a29dc08a3b589516bb5"
uuid = "171d559e-b47b-412a-8079-5efa626c420e"
version = "0.1.15"

[[deps.StaticArrays]]
deps = ["LinearAlgebra", "PrecompileTools", "Random", "StaticArraysCore"]
git-tree-sha1 = "eeafab08ae20c62c44c8399ccb9354a04b80db50"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.9.7"
weakdeps = ["ChainRulesCore", "Statistics"]

    [deps.StaticArrays.extensions]
    StaticArraysChainRulesCoreExt = "ChainRulesCore"
    StaticArraysStatisticsExt = "Statistics"

[[deps.StaticArraysCore]]
git-tree-sha1 = "192954ef1208c7019899fbf8049e717f92959682"
uuid = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
version = "1.4.3"

[[deps.StatisticalTraits]]
deps = ["ScientificTypesBase"]
git-tree-sha1 = "542d979f6e756f13f862aa00b224f04f9e445f11"
uuid = "64bff920-2084-43da-a3e6-9bb72801c0c9"
version = "3.4.0"

[[deps.Statistics]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "ae3bb1eb3bba077cd276bc5cfc337cc65c3075c0"
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
version = "1.11.1"
weakdeps = ["SparseArrays"]

    [deps.Statistics.extensions]
    SparseArraysExt = ["SparseArrays"]

[[deps.StatsAPI]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.7.0"

[[deps.StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "5cf7606d6cef84b543b483848d4ae08ad9832b21"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.34.3"

[[deps.StatsFuns]]
deps = ["HypergeometricFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
git-tree-sha1 = "b423576adc27097764a90e163157bcfc9acf0f46"
uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
version = "1.3.2"
weakdeps = ["ChainRulesCore", "InverseFunctions"]

    [deps.StatsFuns.extensions]
    StatsFunsChainRulesCoreExt = "ChainRulesCore"
    StatsFunsInverseFunctionsExt = "InverseFunctions"

[[deps.StatsModels]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Printf", "REPL", "ShiftedArrays", "SparseArrays", "StatsAPI", "StatsBase", "StatsFuns", "Tables"]
git-tree-sha1 = "9022bcaa2fc1d484f1326eaa4db8db543ca8c66d"
uuid = "3eaba693-59b7-5ba5-a881-562e759f1c8d"
version = "0.7.4"

[[deps.StatsPlots]]
deps = ["AbstractFFTs", "Clustering", "DataStructures", "Distributions", "Interpolations", "KernelDensity", "LinearAlgebra", "MultivariateStats", "NaNMath", "Observables", "Plots", "RecipesBase", "RecipesPipeline", "Reexport", "StatsBase", "TableOperations", "Tables", "Widgets"]
git-tree-sha1 = "3b1dcbf62e469a67f6733ae493401e53d92ff543"
uuid = "f3b207a7-027a-5e70-b257-86293d7955fd"
version = "0.15.7"

[[deps.StructArrays]]
deps = ["ConstructionBase", "DataAPI", "Tables"]
git-tree-sha1 = "f4dc295e983502292c4c3f951dbb4e985e35b3be"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.18"
weakdeps = ["Adapt", "GPUArraysCore", "SparseArrays", "StaticArrays"]

    [deps.StructArrays.extensions]
    StructArraysAdaptExt = "Adapt"
    StructArraysGPUArraysCoreExt = "GPUArraysCore"
    StructArraysSparseArraysExt = "SparseArrays"
    StructArraysStaticArraysExt = "StaticArrays"

[[deps.StyledStrings]]
uuid = "f489334b-da3d-4c2e-b8f0-e476e12c162b"
version = "1.11.0"

[[deps.SuiteSparse]]
deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"

[[deps.SuiteSparse_jll]]
deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
version = "7.7.0+0"

[[deps.SymbolicAnalysis]]
deps = ["DSP", "DataStructures", "Dictionaries", "Distributions", "DomainSets", "IfElse", "LinearAlgebra", "LogExpFunctions", "Manifolds", "PDMats", "RecursiveArrayTools", "StatsBase", "SymbolicUtils", "Symbolics"]
git-tree-sha1 = "64f26bb4a666bb97baa16f063164ade83ca29ec9"
uuid = "4297ee4d-0239-47d8-ba5d-195ecdf594fe"
version = "0.3.0"

[[deps.SymbolicIndexingInterface]]
deps = ["Accessors", "ArrayInterface", "RuntimeGeneratedFunctions", "StaticArraysCore"]
git-tree-sha1 = "4bc96df5d71515b1cb86dd626915f06f4c0d46f5"
uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
version = "0.3.33"

[[deps.SymbolicLimits]]
deps = ["SymbolicUtils"]
git-tree-sha1 = "fabf4650afe966a2ba646cabd924c3fd43577fc3"
uuid = "19f23fe9-fdab-4a78-91af-e7b7767979c3"
version = "0.2.2"

[[deps.SymbolicUtils]]
deps = ["AbstractTrees", "ArrayInterface", "Bijections", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DocStringExtensions", "DynamicPolynomials", "IfElse", "LinearAlgebra", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "TermInterface", "TimerOutputs", "Unityper"]
git-tree-sha1 = "04e9157537ba51dad58336976f8d04b9ab7122f0"
uuid = "d1185830-fcd6-423d-90d6-eec64667417b"
version = "3.7.2"

    [deps.SymbolicUtils.extensions]
    SymbolicUtilsLabelledArraysExt = "LabelledArrays"
    SymbolicUtilsReverseDiffExt = "ReverseDiff"

    [deps.SymbolicUtils.weakdeps]
    LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"

[[deps.Symbolics]]
deps = ["ADTypes", "ArrayInterface", "Bijections", "CommonWorldInvalidations", "ConstructionBase", "DataStructures", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "DynamicPolynomials", "IfElse", "LaTeXStrings", "Latexify", "Libdl", "LinearAlgebra", "LogExpFunctions", "MacroTools", "Markdown", "NaNMath", "PrecompileTools", "Primes", "RecipesBase", "Reexport", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArraysCore", "SymbolicIndexingInterface", "SymbolicLimits", "SymbolicUtils", "TermInterface"]
git-tree-sha1 = "9cd83b6a270bb6135666c4d566cb8d85730ea9e5"
uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
version = "6.14.0"

    [deps.Symbolics.extensions]
    SymbolicsForwardDiffExt = "ForwardDiff"
    SymbolicsGroebnerExt = "Groebner"
    SymbolicsLuxExt = "Lux"
    SymbolicsNemoExt = "Nemo"
    SymbolicsPreallocationToolsExt = ["PreallocationTools", "ForwardDiff"]
    SymbolicsSymPyExt = "SymPy"

    [deps.Symbolics.weakdeps]
    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
    Groebner = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
    Lux = "b2108857-7c20-44ae-9111-449ecde12c47"
    Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
    PreallocationTools = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
    SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"

[[deps.TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.3"

[[deps.TZJData]]
deps = ["Artifacts"]
git-tree-sha1 = "36b40607bf2bf856828690e097e1c799623b0602"
uuid = "dc5dba14-91b3-4cab-a142-028a31da12f7"
version = "1.3.0+2024b"

[[deps.TableOperations]]
deps = ["SentinelArrays", "Tables", "Test"]
git-tree-sha1 = "e383c87cf2a1dc41fa30c093b2a19877c83e1bc1"
uuid = "ab02a1b2-a7df-11e8-156e-fb1833f50b87"
version = "1.2.0"

[[deps.TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[deps.Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "OrderedCollections", "TableTraits"]
git-tree-sha1 = "598cd7c1f68d1e205689b1c2fe65a9f85846f297"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.12.0"

[[deps.Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.0"

[[deps.TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"

[[deps.TermInterface]]
git-tree-sha1 = "d673e0aca9e46a2f63720201f55cc7b3e7169b16"
uuid = "8ea1fca8-c5ef-4a55-8b96-4e9afe9c9a3c"
version = "2.0.0"

[[deps.TerminalLoggers]]
deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
git-tree-sha1 = "f133fab380933d042f6796eda4e130272ba520ca"
uuid = "5d786b92-1e48-4d6f-9151-6b4477ca9bed"
version = "0.1.7"

[[deps.Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
version = "1.11.0"

[[deps.TimeZones]]
deps = ["Dates", "Downloads", "InlineStrings", "Mocking", "Printf", "Scratch", "TZJData", "Unicode", "p7zip_jll"]
git-tree-sha1 = "8323074bc977aa85cf5ad71099a83ac75b0ac107"
uuid = "f269a46b-ccf7-5d73-abea-4c690281aa53"
version = "1.18.1"
weakdeps = ["RecipesBase"]

    [deps.TimeZones.extensions]
    TimeZonesRecipesBaseExt = "RecipesBase"

[[deps.TimerOutputs]]
deps = ["ExprTools", "Printf"]
git-tree-sha1 = "3a6f063d690135f5c1ba351412c82bae4d1402bf"
uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
version = "0.5.25"

[[deps.Tracker]]
deps = ["Adapt", "ChainRulesCore", "DiffRules", "ForwardDiff", "Functors", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NNlib", "NaNMath", "Optimisers", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
git-tree-sha1 = "da45269e1da051c2a13624194fcdc74d6483fad5"
uuid = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
version = "0.2.35"
weakdeps = ["PDMats"]

    [deps.Tracker.extensions]
    TrackerPDMatsExt = "PDMats"

[[deps.TranscodingStreams]]
git-tree-sha1 = "0c45878dcfdcfa8480052b6ab162cdd138781742"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.11.3"

[[deps.Transducers]]
deps = ["Accessors", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "ConstructionBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "SplittablesBase", "Tables"]
git-tree-sha1 = "7deeab4ff96b85c5f72c824cae53a1398da3d1cb"
uuid = "28d57a85-8fef-5791-bfe6-a80928e7c999"
version = "0.4.84"

    [deps.Transducers.extensions]
    TransducersAdaptExt = "Adapt"
    TransducersBlockArraysExt = "BlockArrays"
    TransducersDataFramesExt = "DataFrames"
    TransducersLazyArraysExt = "LazyArrays"
    TransducersOnlineStatsBaseExt = "OnlineStatsBase"
    TransducersReferenceablesExt = "Referenceables"

    [deps.Transducers.weakdeps]
    Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
    BlockArrays = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
    LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
    OnlineStatsBase = "925886fa-5bf2-5e8e-b522-a9147a512338"
    Referenceables = "42d2dcc6-99eb-4e98-b66c-637b7d73030e"

[[deps.Tricks]]
git-tree-sha1 = "7822b97e99a1672bfb1b49b668a6d46d58d8cbcb"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.9"

[[deps.Turing]]
deps = ["ADTypes", "AbstractMCMC", "Accessors", "AdvancedHMC", "AdvancedMH", "AdvancedPS", "AdvancedVI", "BangBang", "Bijectors", "Compat", "DataStructures", "Distributions", "DistributionsAD", "DocStringExtensions", "DynamicPPL", "EllipticalSliceSampling", "ForwardDiff", "Libtask", "LinearAlgebra", "LogDensityProblems", "LogDensityProblemsAD", "MCMCChains", "NamedArrays", "Optimization", "OptimizationOptimJL", "OrderedCollections", "Printf", "Random", "Reexport", "Requires", "SciMLBase", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns"]
git-tree-sha1 = "f69f33f7862a66674c279fe9b86b457a96767e35"
uuid = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
version = "0.34.1"

    [deps.Turing.extensions]
    TuringDynamicHMCExt = "DynamicHMC"
    TuringOptimExt = "Optim"

    [deps.Turing.weakdeps]
    DynamicHMC = "bbc10e6e-7c05-544b-b16e-64fede858acb"
    Optim = "429524aa-4258-5aef-a3af-852621145aeb"

[[deps.URIs]]
git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.5.1"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
version = "1.11.0"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
version = "1.11.0"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unitful]]
deps = ["Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "d95fe458f26209c66a187b1114df96fd70839efd"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.21.0"
weakdeps = ["ConstructionBase", "InverseFunctions"]

    [deps.Unitful.extensions]
    ConstructionBaseUnitfulExt = "ConstructionBase"
    InverseFunctionsUnitfulExt = "InverseFunctions"

[[deps.UnitfulLatexify]]
deps = ["LaTeXStrings", "Latexify", "Unitful"]
git-tree-sha1 = "975c354fcd5f7e1ddcc1f1a23e6e091d99e99bc8"
uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
version = "1.6.4"

[[deps.Unityper]]
deps = ["ConstructionBase"]
git-tree-sha1 = "25008b734a03736c41e2a7dc314ecb95bd6bbdb0"
uuid = "a7c27f48-0311-42f6-a7f8-2c11e75eb415"
version = "0.1.6"

[[deps.UnsafeAtomics]]
git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278"
uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f"
version = "0.2.1"

[[deps.UnsafeAtomicsLLVM]]
deps = ["LLVM", "UnsafeAtomics"]
git-tree-sha1 = "2d17fabcd17e67d7625ce9c531fb9f40b7c42ce4"
uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249"
version = "0.2.1"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.Vulkan_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
version = "1.3.243+0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+1"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.31.0+0"

[[deps.WeakRefStrings]]
deps = ["DataAPI", "InlineStrings", "Parsers"]
git-tree-sha1 = "b1be2855ed9ed8eac54e5caff2afcdb442d52c23"
uuid = "ea10d353-3f73-51f8-a26c-33c1cb351aa5"
version = "1.4.2"

[[deps.Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "fcdae142c1cfc7d89de2d11e08721d0f2f86c98a"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.6"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "c1a7aa6219628fcd757dede0ca95e245c5cd9511"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "1.0.0"

[[deps.WorkerUtilities]]
git-tree-sha1 = "cd1659ba0d57b71a464a29e64dbc67cfe83d54e7"
uuid = "76eceee3-57b5-4d4a-8e66-0e911cebbf60"
version = "1.6.1"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
git-tree-sha1 = "1165b0443d0eca63ac1e32b8c0eb69ed2f4f8127"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.13.3+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "a54ee957f4c86b526460a720dbc882fa5edcbefc"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.41+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "ac88fb95ae6447c8dda6a5503f3bafd496ae8632"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.4.6+0"

[[deps.Xorg_libICE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "326b4fea307b0b39892b3e85fa451692eda8d46c"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.1.1+0"

[[deps.Xorg_libSM_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"]
git-tree-sha1 = "3796722887072218eabafb494a13c963209754ce"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.4+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "d2d1a5c49fae4ba39983f63de6afcbea47194e85"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.6+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "47e45cd78224c53109495b3e324df0c37bb61fbe"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.11+0"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "bcd466676fef0878338c61e655629fa7bbc69d8e"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.17.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.4+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "555d1076590a6cc2fdee2ef1469451f872d8b41b"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.6+1"

[[deps.ZygoteRules]]
deps = ["ChainRulesCore", "MacroTools"]
git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.5"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.9+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "936081b536ae4aa65415d869287d43ef3cb576b2"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.53.0+0"

[[deps.gperf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
version = "3.1.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.9.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "e17c115d55c5fbb7e52ebedb427a0dca79d4484e"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.2+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libdecor_jll]]
deps = ["Artifacts", "Dbus_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pango_jll", "Wayland_jll", "xkbcommon_jll"]
git-tree-sha1 = "9bf7903af251d2050b467f76bdbe57ce541f7f4f"
uuid = "1183f4f0-6f2a-5f1a-908b-139f9cdfea6f"
version = "0.2.2+0"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8a22cf860a7d27e4f3498a0fe0811a7957badb38"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.3+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.18.0+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "b70c870239dc3d7bc094eb2d6be9b73d27bef280"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.44+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "490376214c4721cdaca654041f635213c6165cb3"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+2"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.12.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

# ╔═╡ Cell order:
# ╟─661b028c-260c-41f8-9d8a-13cfea4c7e22
# ╟─bce03358-19c9-11ed-31d9-5b0929af50b6
# ╟─0a8fff98-24fd-49d6-a6b2-061e6350350b
# ╟─ccc43bd4-2149-4136-87f4-a4d251fc1f7a
# ╟─9810605e-586b-4f38-a43c-4240cb91e154
# ╟─f42b1665-df4b-4181-be03-71ccc3dbfae2
# ╟─e752d05f-bc3c-42a4-ac5a-0517637c59b9
# ╟─793a70b2-af69-4b4c-b4c0-8eef3b4654e9
# ╟─af482903-2975-48d7-a4fe-4cebfa337a2b
# ╟─ada4ad28-358e-4144-9d5c-f3b1d27deff1
# ╠═7a189076-f53f-48ed-ace2-ffbcc287ff6f
# ╠═1068259e-a7f6-4a56-b526-59e080c54d27
# ╟─60a5cad4-c676-4334-8cbe-47877a68943f
# ╟─0c70c6be-518b-4ba4-bd69-cc34d2217077
# ╟─cd76fa94-d0d7-43bb-8221-2a4dafa8af53
# ╟─ccda7f54-67ee-4d17-a16c-6f8597447d1e
# ╟─e2918ef9-7f86-4d3b-93cb-65b8b5f48987
# ╟─8b73706e-fe00-4489-8095-b3ec4528c58b
# ╠═6d2af85d-8c9e-4da7-8a38-6c0df102f954
# ╟─8a8d8eb9-9cea-43f0-9607-9d3ca908c370
# ╠═41a3984c-aee4-494f-8ba2-69c0274185ed
# ╠═e1e43074-9e5f-4516-bf0d-0ce4209afb6c
# ╠═15b2d945-4e78-4c41-9712-5d623b15914e
# ╠═5e5fdd62-ac1c-4ef6-a5a4-64ffe441b496
# ╟─bdcc9726-d1fd-4d34-987e-925e1a96e58f
# ╟─fd9d6126-d764-40f5-9a4d-fda49a0962a9
# ╠═69258680-fc21-40ca-998a-1a81279342ea
# ╠═be4d04ff-9ae8-40c6-ae7b-9ec29cd23b43
# ╟─a84e1f2f-fdde-432f-89d3-265480ef9f53
# ╟─44ccb675-a657-4fe8-934f-ddf29cb78f74
# ╟─922704a0-b0c9-4fe0-a0fb-3ab58a7f01d9
# ╟─6aaa775e-b2c4-4943-8860-9aff2e4a725c
# ╟─2a632fe1-698f-4265-8509-453ee7827ae6
# ╟─68b88445-fb94-4d26-a723-234b3045ca54
# ╟─39c43d27-6806-4fb6-a0e8-5f41ae0ee94e
# ╟─436f0628-ee73-4045-82f3-6d785b5ba51f
# ╠═74a2053f-ef53-41df-8afc-997c166e6f67
# ╟─e47c4ad6-17e4-4265-bee2-738b81e61696
# ╟─8b56260f-2e42-4a89-a1c0-bf856b9f75d3
# ╠═40db5082-3558-4fd4-ab47-1127f6d67e38
# ╠═fbcdbc4e-f55b-4bf8-a10d-42f2627dbfdb
# ╟─8c73a18f-55a1-4740-8795-5bbb6ff425de
# ╠═920b9b1f-b56d-465c-bce2-e08530ec4bb4
# ╠═0ca3c752-627f-40ce-ac6c-d10fc90d4663
# ╟─a84de1b9-3c27-4b63-822f-f454b7d3098b
# ╟─b25a3f92-f3ad-4c05-961d-2f69d39d98c3
# ╠═4d9c1339-c38f-4705-9c00-2c99228da905
# ╟─bd11a4c4-1f2b-4d3c-8e3f-8382dd9f3b3c
# ╠═244ba3cf-63ba-4501-8e88-f71c95c15a7c
# ╠═c83f3735-6aba-4183-b010-5f21cd2ff968
# ╟─30d1520d-d301-422a-81e1-a40122d5e3fa
# ╠═53c5b238-61fd-4ef3-9194-b076b3434b16
# ╟─0c34decf-ee35-4f9d-bf83-cfff75f8ff3b
# ╠═f092a42e-16e9-45ac-88cd-133a92402ff6
# ╟─59245146-ef30-4df1-9ac3-776871e5d062
# ╠═ea897f9a-89ff-421c-989a-b5f395cec705
# ╠═78d6fe62-432b-49f3-b38f-0f6f6f5a04ed
# ╠═c92f0602-9a6c-4e2c-8a28-2a870d332fe4
# ╠═82fc962c-a172-47ef-a86c-fa49bace3567
# ╠═3e45f16f-ea6c-4960-98b7-1e642fb919c1
# ╠═8a21c570-9bfe-4f66-9157-1b0dc4028ef4
# ╠═f9b3916a-d4b2-4e6b-9a7d-be077fd45ac0
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002