Wclaer/update notebooks

src/exercises/MCMC_3-advanced.jl

@@ -1,24 +1,23 @@
 ### A Pluto.jl notebook ###
-# v0.20.4
+# v0.20.21
 
 #> [frontmatter]
-#> order = "22"
-#> title = "4. MCMCM advanced"
-#> date = "2025-08-06"
+#> order = "29"
+#> title = "5. MCMC advanced"
 #> tags = ["exercises"]
-#> description = "MCMC advanced"
 #> layout = "layout.jlhtml"
+#> description = "MCMC advanced"
 #> 
 #>     [[frontmatter.author]]
-#>     name = "Gauthier Vanhaelewyn"
+#>     name = "Bram Spanoghe"
 
 using Markdown
 using InteractiveUtils
 
 # This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
 macro bind(def, element)
     #! format: off
-    quote
+    return quote
         local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
         local el = $(esc(element))
         global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
@@ -28,6 +27,8 @@ macro bind(def, element)
 end
 
 # ╔═╡ 75581580-2fb2-4112-b397-2b775eb64630
+# Running this yourself? Point this at your own environment —
+# we advise one shared project in the parent folder: Pkg.activate("..")
 using Pkg; Pkg.activate("../../pluto-deployment-environment")
 
 # ╔═╡ e07a1ae5-43b7-4c12-831d-43e1738eeac0
@@ -52,9 +53,6 @@ At some known timepoints `ts`, we get noisy observations on the car's vertical p
 # ╔═╡ 90f185f3-91d4-4ee7-8de3-b76251c0c169
 ts = 1:10;
 
-# ╔═╡ 852a8d4e-3374-4805-b372-da3e93f4c664
-collect(ts)
-
 # ╔═╡ 599ae818-fb28-4803-b720-9fcf2bb162b7
 ys_obs = [0.6, 0.0, 0.8, -0.7, -0.5, 0.2, 1.0, 1.2, 1.8, 1.1];
 
@@ -72,7 +70,7 @@ md"""
 At some point `t_switch` ∈ [0, 10], the car switches from lane 1 to lane 2. We can describe the model as follows:
 - If `t <= t_switch`, then `y ~ Normal(0.0, σ)`,
 - If `t > t_switch`, then `y ~ Normal(1.0, σ)`,
-with `σ` some (small) noise parameter.
+with `σ` a noise parameter, of which you only know that it's probably small.
 """
 
 # ╔═╡ 0bdac14c-db71-47b5-95d5-d83fb1e68cab
@@ -100,33 +98,11 @@ md"""
 
 # ╔═╡ 70fd793a-3ce3-446f-adc1-65ce0a68e48a
 @model function cars(ts)
-	t_switch ~ Uniform(0, 10)
-	σ ~ Exponential(1.0)
-
-	ys_obs = zeros(length(ts))
-	for pointidx in 1:length(ts)
-		if ts[pointidx] <= t_switch
-			ys_obs[pointidx] ~ Normal(0.0, σ)
-		else
-			ys_obs[pointidx] ~ Normal(1.0, σ)
-		end		
-	end
+	missing
 end
 
-# ╔═╡ 3db9343e-9fb1-4f5c-bbfd-81e5a3623b44
-carmodel = cars(ts) | (ys_obs = ys_obs,)
-
-# ╔═╡ b39b4b09-95ee-49db-924c-0280847b408e
-carchain = sample(carmodel, NUTS(), 2000)
-
-# ╔═╡ 36c7809e-7597-491d-a79e-100cca700597
-plot(carchain)
-
-# ╔═╡ 261e426a-60d6-4dbd-aad5-88a96f408b1d
-histogram(carchain[:t_switch], normalized=:probability)
-
-# ╔═╡ 0c389fd7-35ba-41e1-9154-0c374d996156
-mean(carchain[:t_switch])
+# ╔═╡ fb202b86-c058-4f03-9062-ab282c71d5c4
+missing # histogram of `t_switch`
 
 # ╔═╡ 34bf815a-3bd3-49b5-b06d-d4297ca213a8
 md"## Petridish peril (inference edition)"
@@ -163,57 +139,27 @@ logistic(t, P0, r, K) =  K / (1 + (K - P0)/P0 * exp(-r*t))
 md"### 1"
 
 # ╔═╡ f080f708-a457-40a3-936c-b82d5159975d
-dropletdist = MixtureModel([Poisson(10), Poisson(30)], [0.75, 0.25]);
+dropletdist = missing
 
 # ╔═╡ 7b4aef69-10ec-4935-b7fd-4c1d49aa9b3d
-@model function petrigrowth(t_obs)
-	P0 ~ dropletdist
-    r ~ LogNormal(0.0, 0.3)
-	K ~ Normal(1e5, 1e4)
-
-	logfun = t -> logistic(t, P0, r, K)
-
-	Pt = logfun(t_obs)  # Number of bacteria at the observed time
-    P_obs ~ Poisson(Pt) # The observed number is Poisson distributed
-
-    return logfun
+@model function petrigrowth()
+	missing
 end
 
-# ╔═╡ a5b5a65e-2bac-49fa-b4ca-2fcaf64e4ada
-petrimodel = petrigrowth(5) | (P_obs = 21_000,)
-
-# ╔═╡ b579ccc6-993e-451b-a137-6fff6b630b49
-petrichain = sample(petrimodel, MH(), 100_000) # better and faster than PG(40)
-
-# ╔═╡ 9633f07a-d583-4680-b3cc-f5701540968f
-plot(petrichain)
-
-# ╔═╡ 7d0e5f0b-2cdf-4946-a186-f70774e363bb
-logfuns = generated_quantities(petrimodel, petrichain);
-
-# ╔═╡ c642574c-c01b-4398-aac9-43e514d7fa25
-sp_petri = [logfun(8.0) for logfun in logfuns]
-
-# ╔═╡ d15fa091-839c-4239-96e2-eaf7335ce620
-prob_splittable = mean((sp_petri .>= 1e4) .&& (sp_petri .<= 1e5))
+# ╔═╡ 3e98c640-4bb0-4b5d-bae0-769133a599a7
+prob_splittable = missing
 
 # ╔═╡ 0ea95b67-d4da-4c5a-ad2e-05024ad074a3
 md"### 2"
 
-# ╔═╡ 3d9b73ef-2aae-4c19-bddc-4081927ec92d
-plot(logfuns[1:10:1000], xlims = (0, 12), legend = false, color = :skyblue, alpha = 0.5)
+# ╔═╡ 47b15322-0b8c-48f1-b123-271ebae92655
+missing # plot
 
 # ╔═╡ 9ab88be4-4cf8-4747-ac36-3f1b82899be0
 md"### 3🌟"
 
 # ╔═╡ 113d8311-7bdc-461c-b077-920e23b33d39
-dropletdist🌟 = MixtureModel(
-	[
-		truncated(Normal(10, sqrt(10)), lower = 0.0),
-		truncated(Normal(30, sqrt(30)), lower = 0.0)
-	],
-	[0.75, 0.25]
-);
+dropletdist🌟 = missing
 
 # ╔═╡ 4e730df9-f619-464a-b8a3-57448132404b
 begin
@@ -223,31 +169,12 @@ begin
 end
 
 # ╔═╡ d9b50958-20ae-4085-80d6-19420c7d89df
-@model function petrigrowth🌟(t_obs)
-	P0 ~ dropletdist🌟
-    r ~ LogNormal(0.0, 0.3)
-	K ~ Normal(1e5, 1e4)
-
-	logfun = t -> logistic(t, P0, r, K)
-	Pt = logfun(t_obs)
-    P_obs ~ Poisson(Pt)
-
-    return logfun
-end
-
-# ╔═╡ 9ac7aa12-d945-4078-ae63-d598d7171112
-let # so we dont need to rename all variables
-	petrimodel = petrigrowth🌟(5) | (P_obs = 21_000,)
-	petrichain = sample(petrimodel, NUTS(), 2_000)
-	logfuns = generated_quantities(petrimodel, petrichain);
-	sp_petri = [logfun(8.0) for logfun in logfuns]
-	prob_splittable = mean((sp_petri .>= 1e4) .&& (sp_petri .<= 1e5))
-	println("The new `prob_splittable` is ", prob_splittable)
-	plot(petrichain)
+@model function petrigrowth🌟()
+	missing
 end
 
-# ╔═╡ 2f4308df-4451-4ac2-8a31-65cd49a275af
-md"Changing to all continuous distributions made the inference much higher quality in this case, as can be seen from the chain plots. This also means this result is more reliable!"
+# ╔═╡ 0704ed4d-5b3e-401d-a496-98782cb20b09
+prob_splittable🌟 = missing
 
 # ╔═╡ Cell order:
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@@ -257,7 +184,6 @@ md"Changing to all continuous distributions made the inference much higher quali
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@@ -266,11 +192,7 @@ md"Changing to all continuous distributions made the inference much higher quali
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-# ╠═b39b4b09-95ee-49db-924c-0280847b408e
-# ╠═36c7809e-7597-491d-a79e-100cca700597
-# ╠═261e426a-60d6-4dbd-aad5-88a96f408b1d
-# ╠═0c389fd7-35ba-41e1-9154-0c374d996156
+# ╠═fb202b86-c058-4f03-9062-ab282c71d5c4
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@@ -279,17 +201,11 @@ md"Changing to all continuous distributions made the inference much higher quali
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-# ╠═9633f07a-d583-4680-b3cc-f5701540968f
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-# ╠═c642574c-c01b-4398-aac9-43e514d7fa25
-# ╠═d15fa091-839c-4239-96e2-eaf7335ce620
+# ╠═3e98c640-4bb0-4b5d-bae0-769133a599a7
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-# ╠═3d9b73ef-2aae-4c19-bddc-4081927ec92d
+# ╠═47b15322-0b8c-48f1-b123-271ebae92655
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-# ╟─2f4308df-4451-4ac2-8a31-65cd49a275af
+# ╠═0704ed4d-5b3e-401d-a496-98782cb20b09