diff --git a/_quarto.yml b/_quarto.yml index b33479b0a..720098fc0 100644 --- a/_quarto.yml +++ b/_quarto.yml @@ -202,3 +202,6 @@ using-turing-abstractmcmc: developers/inference/abstractmcmc-turing using-turing-interface: developers/inference/abstractmcmc-interface using-turing-variational-inference: developers/inference/variational-inference using-turing-implementing-samplers: developers/inference/implementing-samplers +dev-transforms-distributions: developers/transforms/distributions +dev-transforms-bijectors: developers/transforms/bijectors +dev-transforms-dynamicppl: developers/transforms/dynamicppl diff --git a/developers/transforms/bijectors/index.qmd b/developers/transforms/bijectors/index.qmd index 3a31d4f3c..e8c8bb840 100644 --- a/developers/transforms/bijectors/index.qmd +++ b/developers/transforms/bijectors/index.qmd @@ -28,6 +28,7 @@ A _bijection_ between two sets ([Wikipedia](https://en.wikipedia.org/wiki/Biject That is to say, if we have two sets $X$ and $Y$, then a bijection maps each element of $X$ to a unique element of $Y$. To return to our univariate example, where we transformed $x$ to $y$ using $y = \exp(x)$, the exponentiation function is a bijection because every value of $x$ maps to one unique value of $y$. The input set (the domain) is $(-\infty, \infty)$, and the output set (the codomain) is $(0, \infty)$. +(Here, $(a, b)$ denotes the open interval from $a$ to $b$ but excluding $a$ and $b$ themselves.) Since bijections are a one-to-one mapping between elements, we can also reverse the direction of this mapping to create an inverse function. In the case of $y = \exp(x)$, the inverse function is $x = \log(y)$. @@ -45,8 +46,8 @@ For example, taking the inverse function $\log(y)$ from above, its derivative is However, we specified that the bijection $y = \exp(x)$ maps values of $x \in (-\infty, \infty)$ to $y \in (0, \infty)$, so the point $y = 0$ is not within the domain of the inverse function. ::: -Specifically, one of the primary purposes of Bijectors.jl is used to construct _bijections which map constrained distributions to unconstrained ones_. -For example, the log-normal distribution which we saw above is constrained: its _support_, i.e. the range over which $p(x) > 0$, is $(0, \infty)$. +Specifically, one of the primary purposes of Bijectors.jl is to construct _bijections which map constrained distributions to unconstrained ones_. +For example, the log-normal distribution which we saw in [the previous page]({{< meta dev-transforms-distributions >}}) is constrained: its _support_, i.e. the range over which $p(x) > 0$, is $(0, \infty)$. However, we can transform that to an unconstrained distribution (the normal distribution) using the transformation $y = \log(x)$. ::: {.callout-note}