Merge pull request #145 from Vaibhavdixit02/bayesupdate

Update and add timings bayes parameter estimation

Author: ChrisRackauckas

Project.toml

@@ -55,7 +55,7 @@ Cairo = "0.8, 1.0"
 CuArrays = "1.4, 2.0"
 DecFP = "0.4"
 Decimals = "0.4"
-DiffEqBayes = "2.1"
+DiffEqBayes = "2.8"
 DiffEqBiological = "4.0"
 DiffEqCallbacks = "2.9"
 DiffEqDevTools = "2.15"

tutorials/models/06-pendulum_bayesian_inference.jmd

@@ -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`
@@ -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,
@@ -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))
+```
+