This repository is a set of extension functionality for estimating the parameters of differential equations using Stan-based Bayesian methods as available in StanSample.jl to perform a Bayesian estimation of a differential equation problem specified via the DifferentialEquations.jl interface.
This repository is a simplification of DiffEqBayes.jl. While DiffEqBayes provides and shows how to run the same problem on multiple mcmc implementations available in Julia, this packages only supports Stan.
Version v3.0.0 is a breaking change with v2.x.x in that is assumes cmdstan has been compiled with
By default 8 CPP threads are used and 4 CPP chains.
To begin you first need to add this repository using the following command:
Pkg.add("DiffEqBayesStan") using DiffEqBayesStan
Tutorials and Documentation
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 StanSample #required for using the Stan backend bayesian_result_stan = stan_inference(prob1,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=) randomized = VectorOfArray([(sol(t[i]) + σ * randn(1)) for i in 1:length(t)]) data = convert(Array,randomized) using StanSample #required for using the Stan backend bayesian_result_stan = stan_inference(prob1,t,data,priors,save_idxs=)