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DiffEqBayes

Extension functionality which uses Stan.jl, DynamicHMC.jl, and Turing.jl to estimate the parameters to differential equations and perform Bayesian probabilistic scientific machine learning

Readme

DiffEqBayes.jl

Build Status Coverage Status codecov.io Stable Dev

This repository is a set of extension functionality for estimating the parameters of differential equations using Bayesian methods. It allows the choice of using CmdStan.jl, Turing.jl, DynamicHMC.jl and ApproxBayes.jl to perform a Bayesian estimation of a differential equation problem specified via the DifferentialEquations.jl interface.

To begin you first need to add this repository using the following command.

Pkg.add("DiffEqBayes")
using DiffEqBayes

Tutorials and Documentation

For information on using the package, see the stable documentation. Use the in-development documentation for the version of the documentation, which contains the unreleased features.

Example

 using ParameterizedFunctions, OrdinaryDiffEq, RecursiveArrayTools, Distributions
 f1 = @ode_def LotkaVolterra begin
  dx = a*x - x*y
  dy = -3*y + x*y
 end a

 p = [1.5]
 u0 = [1.0,1.0]
 tspan = (0.0,10.0)
 prob1 = ODEProblem(f1,u0,tspan,p)

 σ = 0.01                         # noise, fixed for now
 t = collect(1.:10.)   # observation times
 sol = solve(prob1,Tsit5())
 priors = [Normal(1.5, 1)]
 randomized = VectorOfArray([(sol(t[i]) + σ * randn(2)) for i in 1:length(t)])
 data = convert(Array,randomized)

 using CmdStan #required for using the Stan backend
 bayesian_result_stan = stan_inference(prob1,t,data,priors)

 bayesian_result_turing = turing_inference(prob1,Tsit5(),t,data,priors)

 using DynamicHMC #required for DynamicHMC backend
 bayesian_result_hmc = dynamichmc_inference(prob1, Tsit5(), t, data, priors)

 bayesian_result_abc = abc_inference(prob1, Tsit5(), t, data, priors)

Using save_idxs to declare observables

You don't always have data for all of the variables of the model. In case of certain latent variables you can utilise the save_idxs kwarg to declare the oberved variables and run the inference using any of the backends as shown below.

 sol = solve(prob1,Tsit5(),save_idxs=[1])
 randomized = VectorOfArray([(sol(t[i]) + σ * randn(1)) for i in 1:length(t)])
 data = convert(Array,randomized)

 using CmdStan #required for using the Stan backend
 bayesian_result_stan = stan_inference(prob1,t,data,priors,save_idxs=[1])

 bayesian_result_turing = turing_inference(prob1,Tsit5(),t,data,priors,save_idxs=[1])

 using DynamicHMC #required for DynamicHMC backend
 bayesian_result_hmc = dynamichmc_inference(prob1,Tsit5(),t,data,priors,save_idxs = [1])

 bayesian_result_abc = abc_inference(prob1,Tsit5(),t,data,priors,save_idxs=[1])

First Commit

07/24/2017

Last Touched

10 days ago

Commits

526 commits

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