Add DiffEqBayes tutorial markdown, script, html and notebook

notebook/models/06-pendulum_bayesian_inference.ipynb

@@ -3,15 +3,15 @@
     {
       "cell_type": "markdown",
       "source": [
-        "# Bayesian Inference on a Pendulum using Turing.jl\n### Vaibhav Dixit\n\n### Set up simple pendulum problem"
+        "# Bayesian Inference on a Pendulum using DiffEqBayes.jl\n### Vaibhav Dixit\n\n### Set up simple pendulum problem"
       ],
       "metadata": {}
     },
     {
       "outputs": [],
       "cell_type": "code",
       "source": [
-        "using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots"
+        "using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots, BenchmarkTools, TransformVariables, CmdStan, DynamicHMC"
       ],
       "metadata": {},
       "execution_count": null
@@ -99,7 +99,7 @@
     {
       "cell_type": "markdown",
       "source": [
-        "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!"
       ],
       "metadata": {}
     },
@@ -147,9 +147,36 @@
     {
       "cell_type": "markdown",
       "source": [
-        "Notice that after awhile these chains converge to a \"fuzzy line\", meaning it\nfound the area with the most likelihood and then starts to sample around there,\nwhich builds a posterior distribution around the true mean."
+        "Notice that after awhile these chains converge to a \"fuzzy line\", meaning it\nfound the area with the most likelihood and then starts to sample around there,\nwhich builds a posterior distribution around the true mean.\n\nDiffEqBayes.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.\nLet'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\nspecific to each package and algorithm combinations, you might want to do your own experiments for specific problems to get better understanding of the performance."
       ],
       "metadata": {}
+    },
+    {
+      "outputs": [],
+      "cell_type": "code",
+      "source": [
+        "@btime bayesian_result = turing_inference(prob1,Tsit5(),t,data,priors;syms = [:omega,:L],num_samples=10_000)"
+      ],
+      "metadata": {},
+      "execution_count": null
+    },
+    {
+      "outputs": [],
+      "cell_type": "code",
+      "source": [
+        "@btime bayesian_result = stan_inference(prob1,t,data,priors;num_samples=10_000,printsummary=false)"
+      ],
+      "metadata": {},
+      "execution_count": null
+    },
+    {
+      "outputs": [],
+      "cell_type": "code",
+      "source": [
+        "@btime bayesian_result = dynamichmc_inference(prob1,Tsit5(),t,data,priors;num_samples = 10_000)"
+      ],
+      "metadata": {},
+      "execution_count": null
     }
   ],
   "nbformat_minor": 2,
@@ -158,11 +185,11 @@
       "file_extension": ".jl",
       "mimetype": "application/julia",
       "name": "julia",
-      "version": "1.1.1"
+      "version": "1.4.0"
     },
     "kernelspec": {
-      "name": "julia-1.1",
-      "display_name": "Julia 1.1.1",
+      "name": "julia-1.4",
+      "display_name": "Julia 1.4.0",
       "language": "julia"
     }
   },

script/models/06-pendulum_bayesian_inference.jl

@@ -1,5 +1,5 @@
 
-using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots
+using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots, BenchmarkTools, TransformVariables, CmdStan, DynamicHMC
 
 
 function pendulum(du,u,p,t)
@@ -38,3 +38,12 @@ plot(bayesian_result)
 
 plot(bayesian_result, colordim = :parameter)
 
+
+@btime bayesian_result = turing_inference(prob1,Tsit5(),t,data,priors;syms = [:omega,:L],num_samples=10_000)
+
+
+@btime bayesian_result = stan_inference(prob1,t,data,priors;num_samples=10_000,printsummary=false)
+
+
+@btime bayesian_result = dynamichmc_inference(prob1,Tsit5(),t,data,priors;num_samples = 10_000)
+

tutorials/models/06-pendulum_bayesian_inference.jmd

@@ -6,7 +6,7 @@ author: Vaibhav Dixit
 ### Set up simple pendulum problem
 
 ```julia
-using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots, BenchmarkTools, TransformVariables
+using DiffEqBayes, OrdinaryDiffEq, RecursiveArrayTools, Distributions, Plots, StatsPlots, BenchmarkTools, TransformVariables, CmdStan, DynamicHMC
 ```
 
 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 with the Turing.jl backend to check if we indeed recover the parameters! 
+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,
@@ -105,19 +105,18 @@ 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 
+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)
+@btime bayesian_result = stan_inference(prob1,t,data,priors;num_samples=10_000,printsummary=false)
 ```
 
 ```julia
-@btime bayesian_result = dynamichmc_inference(prob1,Tsit5(),t,data,priors,as(Vector, asℝ₊, 1))
+@btime bayesian_result = dynamichmc_inference(prob1,Tsit5(),t,data,priors;num_samples = 10_000)
 ```
-