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# DiffEqBayes.jl

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.

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])

07/24/2017

10 days ago

526 commits