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Update and add timings bayes parameter estimation #145

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Apr 4, 2020
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Update and add timings bayes parameter estimation #145

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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -55,7 +55,7 @@ Cairo = "0.8, 1.0"
CuArrays = "1.4"
DecFP = "0.4"
Decimals = "0.4"
DiffEqBayes = "2.1"
DiffEqBayes = "2.8"
DiffEqBiological = "4.0"
DiffEqCallbacks = "2.9"
DiffEqDevTools = "2.15"
Expand Down
23 changes: 20 additions & 3 deletions tutorials/models/06-pendulum_bayesian_inference.jmd
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@@ -1,12 +1,12 @@
---
title: Bayesian Inference on a Pendulum using Turing.jl
title: Bayesian Inference on a Pendulum using DiffEqBayes.jl
author: Vaibhav Dixit
---

### Set up simple pendulum problem

```julia
using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots
using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots, BenchmarkTools, TransformVariables
```

Let's define our simple pendulum problem. Here our pendulum has a drag term `ω`
Expand Down Expand Up @@ -76,7 +76,7 @@ length of the pendulum L is probably around 3.0:
priors = [Uniform(0.1,3.0), Normal(3.0,1.0)]
```

Finally let's run the estimation routine from DiffEqBayes.jl using the Turing.jl backend
Finally let's run the estimation routine from DiffEqBayes.jl with the Turing.jl backend to check if we indeed recover the parameters!

```julia
bayesian_result = turing_inference(prob1,Tsit5(),t,data,priors;num_samples=10_000,
Expand Down Expand Up @@ -104,3 +104,20 @@ plot(bayesian_result, colordim = :parameter)
Notice that after awhile these chains converge to a "fuzzy line", meaning it
found the area with the most likelihood and then starts to sample around there,
which builds a posterior distribution around the true mean.

DiffEqBayes.jl allows the choice of using Stan.jl, Turing.jl and DynamicHMC.jl for MCMC, you can also use ApproxBayes.jl for Approximate Bayesian computation algorithms.
Let's compare the timings across the different MCMC backends. We'll stick with the default arguments and 10,000 samples in each since there is a lot of room for micro-optimization
specific to each package and algorithm combinations, you might want to do your own experiments for specific problems to get better understanding of the performance.

```julia
@btime bayesian_result = turing_inference(prob1,Tsit5(),t,data,priors;syms = [:omega,:L],num_samples=10_000)
```

```julia
@btime bayesian_result = stan_inference(prob1,t,data,priors;num_samples=10_000)
```

```julia
@btime bayesian_result = dynamichmc_inference(prob1,Tsit5(),t,data,priors,as(Vector, asℝ₊, 1))
```