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Fixes to Bayes SDE notebook #449

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merged 2 commits into from
May 27, 2024
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Fixes to Bayes SDE notebook #449

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6a5da97
Updated retcode success check to the current version used by SciMLBas…
May 24, 2024
44885f2
Added more explanation on the likelihood calculation
May 27, 2024
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28 changes: 19 additions & 9 deletions tutorials/10-bayesian-stochastic-differential-equations/index.qmd
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Original file line number Diff line number Diff line change
Expand Up @@ -17,6 +17,7 @@ Pkg.instantiate();
```{julia}
using Turing
using DifferentialEquations
using DifferentialEquations.EnsembleAnalysis

# Load StatsPlots for visualizations and diagnostics.
using StatsPlots
Expand Down Expand Up @@ -117,6 +118,10 @@ prob_sde = SDEProblem(lotka_volterra!, multiplicative_noise!, u0, tspan, p)
ensembleprob = EnsembleProblem(prob_sde)
data = solve(ensembleprob, SOSRI(); saveat=0.1, trajectories=1000)
plot(EnsembleSummary(data))

# We generate new noisy observations based on the stochastic model for the parameter estimation tasks in this tutorial.
# We create our observations by adding random normally distributed noise to the mean of the ensemble simulation.
sdedata = reduce(hcat, timeseries_steps_mean(data).u) + 0.8 * randn(size(reduce(hcat, timeseries_steps_mean(data).u)))
```

```{julia}
Expand All @@ -132,17 +137,23 @@ plot(EnsembleSummary(data))

# Simulate stochastic Lotka-Volterra model.
p = [α, β, γ, δ, ϕ1, ϕ2]
predicted = solve(prob, SOSRI(); p=p, saveat=0.1)
remake(prob, p = p)
ensembleprob = EnsembleProblem(prob)
predicted = solve(ensembleprob, SOSRI(); saveat=0.1, trajectories = 1000)

# Early exit if simulation could not be computed successfully.
if predicted.retcode !== :Success
Turing.@addlogprob! -Inf
return nothing
for i in 1:length(predicted)
if !SciMLBase.successful_retcode(predicted[i])
Turing.@addlogprob! -Inf
return nothing
end
end

# Observations.
for i in 1:length(predicted)
data[:, i] ~ MvNormal(predicted[i], σ^2 * I)
for j in 1:length(predicted)
for i in 1:length(predicted[j])
data[:, i] ~ MvNormal(predicted[j][i], σ^2 * I)
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Consider adding a bit of explanation on the reasoning behind this likelihood function, e.g. following discussions in TuringLang/Turing.jl#2216

end
end

return nothing
Expand All @@ -154,9 +165,8 @@ Therefore we use NUTS with a low target acceptance rate of `0.25` and specify a
SGHMC might be a more suitable algorithm to be used here.

```{julia}
model_sde = fitlv_sde(odedata, prob_sde)
model_sde = fitlv_sde(sdedata, prob_sde)

setadbackend(:forwarddiff)
chain_sde = sample(
model_sde,
NUTS(0.25),
Expand All @@ -165,4 +175,4 @@ chain_sde = sample(
progress=false,
)
plot(chain_sde)
```
```