Bs/stability fixes

exercises/solved_notebooks/P5_mcmc/MCMC_2-basics.jl

@@ -62,7 +62,7 @@ md"### 2: Unconditional expected value of Y"
 
 # ╔═╡ 3decb2ec-210a-4b2f-842d-6fd40dd3f77b
 @model function mole()
-	X ~ X_prior
+	X ~ Exponential(100)
 	Y ~ Uniform(0, X)
 	return Y
 end
@@ -108,7 +108,7 @@ md"### 5: Conditional distribution of X (with more data)"
 
 # ╔═╡ b2b16c34-e12a-4bea-8098-313d01913bbf
 @model function mole2()
-	X ~ X_prior
+	X ~ Exponential(100)
 	Ys = zeros(4)
 	for i in 1:length(Ys)
 		Ys[i] ~ Uniform(0, X)
@@ -245,7 +245,7 @@ md"### 3: Conditional expected value"
 
 # ╔═╡ 126d3954-c77d-4c98-abe0-fd87d14e6265
 @model function lights()
-	μ ~ lights_prior
+	μ ~ LogNormal(log(40), 0.5)
 	lifespans = zeros(4)
 	for i in 1:length(lifespans)
 		lifespans[i] ~ Exponential(μ)
@@ -284,7 +284,7 @@ md"""
 
 # ╔═╡ 8fc58fa4-b005-4f32-9eae-a8143582a1ae
 @model function lights_censored(time_observed, n_working)
-	μ ~ lights_prior
+	μ ~ LogNormal(log(40), 0.5)
 
 	lifespans = zeros(2)
 	for i in 1:length(lifespans)

exercises/solved_notebooks/P5_mcmc/MCMC_3-advanced.jl

@@ -211,12 +211,18 @@ end
 
 # ╔═╡ d9b50958-20ae-4085-80d6-19420c7d89df
 @model function petrigrowth🌟(t_obs)
-	P0 ~ dropletdist🌟
+	P0 ~ MixtureModel(
+		[
+			truncated(Normal(10, sqrt(10)), lower = 0.0),
+			truncated(Normal(30, sqrt(30)), lower = 0.0)
+		],
+		[0.75, 0.25]
+	)
     r ~ LogNormal(0.0, 0.3)
 	K ~ Normal(1e5, 1e4)
 
 	logfun = t -> logistic(t, P0, r, K)
-	Pt = logfun(t_obs)
+	Pt = max(logfun(t_obs), 0) # set to 0 if negative to prevent possible errors (not required)
     P_obs ~ Poisson(Pt)
 
     return logfun

exercises/solved_notebooks/P6_calib/calib_fermenter_monod_sol.jl

@@ -113,34 +113,23 @@ Furthermore, suppose that at $t = 0\;h$ no substrate $S$ is present in the react
 Calibrate the parameter values for $\mu_{max}$ and $K_s$ using the aforementioned measurement data for $S$ and $X$ in a timespan of `[0, 100]`$\mathrm{h}$. Take the values above as initial values for $\mu_{max}$ and $K_s$.
 """
 
-# ╔═╡ 7a227eaf-18d0-44f4-ac4b-f529e81c7471
-md"""
-Create an `ODEProblem`. Use the aforementioned values as initial values for the problem.
-"""
-
-# ╔═╡ 6375478f-1af9-4fd2-b6f3-101a6f796f2d
+# ╔═╡ 1689c839-9aa5-4bff-a26f-0c8fbf47aa32
 # u0 = missing
 u0 = [:S=>0.0, :X=>0.0005]
 
-# ╔═╡ 38fe8304-af61-40a7-ac86-480dfb892185
+# ╔═╡ 3fbc29b0-c299-4223-9922-d6fb9a4a6a90
 # tspan = missing
 tspan = (0.0, 100)
 
-# ╔═╡ 87482f88-8413-4820-9613-7941f3d61bd7
-# parms = missing
-parms = [:μmax=>0.40, :Ks=>0.015, :Y=>0.67, :Q=>2, :V=>40, :Sin=>0.022]
-
-# ╔═╡ 94f3bd7b-5c2c-4661-a0ab-2cdaf2cd6743
-# oprob = missing
-oprob = ODEProblem(fermenter_monod, u0, tspan, parms, combinatoric_ratelaws=false)
-
 # ╔═╡ f6a8f134-6db0-4d74-8af5-82826347d8f0
 md"""
-Declare the Turing model. Use `InverseGamma()` for the standard deviations of the measurements and `LogNormal()` for `μmax` and `Ks`.
+Declare the Turing model. Assume the following for the priors:
+- The measurement error is an unknown positive value, but probably near $0$.
+- The parameters `μmax` and `K` are both positive and expected to be in $[0.0, 1.0]$, presumably around $0.1$.
 """
 
 # ╔═╡ 4c28a66a-ee2c-42a2-95c7-ea4ddb6a232d
-# @model function fermenter_inference(t_meas, S, X)
+# @model function fermenter_inference(t_meas)
     # σ_S ~ missing
     # σ_X ~ missing
     # μmax ~ missing
@@ -151,34 +140,40 @@ Declare the Turing model. Use `InverseGamma()` for the standard deviations of th
     # S ~ missing
     # X ~ missing
 # end
-@model function fermenter_inference(t_meas, S, X)
-	σ_S ~ InverseGamma()
-	σ_X ~ InverseGamma()
-    μmax ~ LogNormal()
-	Ks ~ LogNormal()
-    parms = [:μmax=>μmax, :Ks=>Ks, :Y=>0.67, :Q=>2, :V=>40, :Sin=>0.022]
-	oprob = ODEProblem(fermenter_monod, u0, tspan, parms, combinatoric_ratelaws=false)
-    osol = solve(oprob, Tsit5(), saveat=t_meas)
-	S ~ MvNormal(osol[:S], σ_S^2 * I)
-	X ~ MvNormal(osol[:X], σ_X^2 * I)
+@model function fermenter_inference(t_meas)
+	σ_S ~ Exponential()
+	σ_X ~ Exponential()
+    μmax ~ LogNormal(log(0.1))
+	Ks ~ LogNormal(log(0.1))
+    parms = [:μmax => μmax, :Ks => Ks, :Y => 0.67, :Q => 2, :V => 40, :Sin => 0.022]
+	oprob = ODEProblem(fermenter_monod, u0, tspan, parms)
+    osol = solve(oprob, AutoTsit5(Rosenbrock23()), saveat=t_meas)
+	S ~ MvNormal(osol[:S], σ_S)
+	X ~ MvNormal(osol[:X], σ_X)
 end
 
+# ╔═╡ c2120cce-5cae-42e5-b1c6-1d10b49d9ffc
+md"""
+!!! tip
+	This model can change between being non-stiff and stiff based on the sampled parameter values. You can use an auto-switching solver such as `AutoTsit5(Rosenbrock23())` here to make calibration more stable.
+"""
+
 # ╔═╡ 3136b15d-5078-4bcd-954b-e89bcb8aed1b
 md"""
 Provide the measurements to the Turing model.
 """
 
 # ╔═╡ 6a508a62-61b9-4273-8e45-b26f594e8da9
 # fermenter_inf = missing
-fermenter_inf = fermenter_inference(t_meas, S_meas, X_meas)
+fermenter_inf = fermenter_inference(t_meas) | (S = S_meas, X = X_meas)
 
 # ╔═╡ 63420055-55f8-4def-8b0e-11ea61483010
 md"""
-Optimize the priors ($\sigma_S$, $\sigma_X$, $\mu_{max}$ and $K_s$). Do this with `MLE` method and Nelder-Mead. Store the optimization results in `results_mle`.
+Optimize the likelihood of the parameters ($\sigma_S$, $\sigma_X$, $\mu_{max}$ and $K_s$) using the NelderMead optimizer. Store the optimization results in `results_mle`.
 """
 
 # ╔═╡ d52c9da8-d8a4-4db0-ac6d-6d16ccf4775c
-# results_map = missing
+# results_mle = missing           # Uncomment and complete the instruction
 results_mle = optimize(fermenter_inf, MLE(), NelderMead())
 
 # ╔═╡ e1b0ee01-f16c-40e9-a0f9-80072d690936
@@ -223,8 +218,8 @@ Create an ODEProblem and solve it. Use `Tsit5()` and `saveat=0.5`.
 """
 
 # ╔═╡ 853c1a92-d50f-4b05-9ed3-d3ee1656665a
-# oprob_opt = missing
-oprob_opt = ODEProblem(fermenter_monod, u0, tspan, parms_opt, combinatoric_ratelaws=false)
+# oprob_opt = missing         # Uncomment and complete the instruction
+oprob_opt = ODEProblem(fermenter_monod, u0, tspan, parms_opt)
 
 # ╔═╡ f45e8124-e942-438e-99c5-3032ccc01454
 # osol_opt = missing
@@ -266,13 +261,11 @@ end
 # ╟─6c481447-28c6-4530-bf2c-64762121bc71
 # ╠═918fd524-81fa-4aff-a403-37402e47235b
 # ╟─ef977370-06ee-4a73-85e2-609a744167d3
-# ╟─7a227eaf-18d0-44f4-ac4b-f529e81c7471
-# ╠═6375478f-1af9-4fd2-b6f3-101a6f796f2d
-# ╠═38fe8304-af61-40a7-ac86-480dfb892185
-# ╠═87482f88-8413-4820-9613-7941f3d61bd7
-# ╠═94f3bd7b-5c2c-4661-a0ab-2cdaf2cd6743
+# ╠═1689c839-9aa5-4bff-a26f-0c8fbf47aa32
+# ╠═3fbc29b0-c299-4223-9922-d6fb9a4a6a90
 # ╟─f6a8f134-6db0-4d74-8af5-82826347d8f0
 # ╠═4c28a66a-ee2c-42a2-95c7-ea4ddb6a232d
+# ╟─c2120cce-5cae-42e5-b1c6-1d10b49d9ffc
 # ╟─3136b15d-5078-4bcd-954b-e89bcb8aed1b
 # ╠═6a508a62-61b9-4273-8e45-b26f594e8da9
 # ╟─63420055-55f8-4def-8b0e-11ea61483010