update

lf28 · Dec 2, 2023 · e566a89 · e566a89
1 parent e8c2e89
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diff --git a/lectures/lecture_bayes2.jl b/lectures/lecture_bayes2.jl
@@ -431,27 +431,15 @@ vline!([mean(Beta(3+7, 3+3))], color=3, ls=:dash, lw=2, label="")
 end)
 """
 
-# ╔═╡ 9638d082-5b61-4051-912b-fc263abeb239
-begin
-	# simulate 200 tosses of a fair coin
-	N_tosses = 200
-	true_θ = 0.5
-	Random.seed!(100)
-	coin_flipping_data = rand(N_tosses) .< true_θ
-	Nh = sum(coin_flipping_data)
-	Nt = N_tosses- Nh
-end;
-
 # ╔═╡ 30ece808-4852-4cbd-84c5-7e8087753ad5
 md"""
-## Sequential update.
+## Sequential update
 
 
 Conjugate prior also provides us with a simple procedure to do **sequential** inference
 
 
 * *sequential online learning:* update the posterior incrementally as data arrives
-* based on the conditional independence assumption
 
 ```math
 \begin{align}
@@ -463,6 +451,7 @@ p(\theta|\{d_1, d_2, \ldots, d_N\})&\propto  p(\theta) \prod_{n=1}^N p(d_n|\thet
 
 * *yesterday's posterior becomes today's prior*
 
+## Sequential update*
 
 To be more specific, the sequential update algorithm is:
 
@@ -477,12 +466,21 @@ $$a_n = a_{n-1} + \mathbf{1}(d_n=\texttt{head}), \;\; b_n = b_{n-1} +  \mathbf{1
 
 Note that the function ``\mathbf{1}(\cdot)`` returns 1 if the test result of the argument is true and 0 otherwise. 
 
-## Demonstration
+## Demonstration: 200 coin tosses
 
-A demon with $(N_tosses) tosses of 
-* a fair coin 
 """
 
+# ╔═╡ 9638d082-5b61-4051-912b-fc263abeb239
+begin
+	# simulate 200 tosses of a fair coin
+	N_tosses = 200
+	true_θ = 0.5
+	Random.seed!(100)
+	coin_flipping_data = rand(N_tosses) .< true_θ
+	Nh = sum(coin_flipping_data)
+	Nt = N_tosses- Nh
+end;
+
 # ╔═╡ 997d45bf-cdbf-4881-b823-ebb7d9ec19db
 let
 	a₀, b₀ = 1, 1
@@ -717,6 +715,12 @@ let
 	# end
 end
 
+# ╔═╡ 29a49584-3a52-410e-8f15-1d9293955826
+md"""
+
+# Bayesian predictive checks
+"""
+
 # ╔═╡ 6b460036-890d-4364-aac2-2c61dc44ed75
 md"""
 
@@ -2805,6 +2809,7 @@ version = "1.4.1+1"
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