DiffEqBayesStan.jl

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 STAN_THREADS=true. 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

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 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.

```julia 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 StanSample #required for using the Stan backend bayesianresultstan = staninference(prob1,t,data,priors,saveidxs=[1]) ```

Create and compile a SampleModel based on DiffEqBayes.

SampleModel(name, prob, t, data)
SampleModel(name, prob, t, data, priors)
SampleModel(
    name,
    prob,
    t,
    data,
    priors,
    stanmodel;
    likelihood,
    vars,
    sample_u0,
    save_idxs,
    diffeq_string,
    alg,
    reltol,
    abstol,
    maxiter,
    tmpdir
)

Extended help

Required positional arguments

* `name::AbstractString` # Name for model
* `prob::DiffEqBase.DEProblem` # Name for the model
* `t` # Time steps
* `data` # Data for DiffEq model

Optional positional arguments

* `priors=nothing`
* `SampleModel=nothing`

Keyword arguments

* `likelihood=Normal`
* `vars=(StanODEData(), InverseGamma(3,3))`
* `sample_u0=false`
* `save_idxs=nothing`
* `diffeq_string=nothing`
* `alg = :rk45`
* `reltol=1e-3`
* `abstol=1e-6`
* `maxiter=Int(1e5)`
* `tmpdir=mktempdir()` # Directory where output files are stored

Returns

* `(samplemodel, data)` # Tuple of SampleModel and data for stan_sample(...)

debs_datadir

Relative path using the StatisticalRethinking src/ directory.

Example to access Howell1.csv in StatisticalRethinking:

df = CSV.read(sr_datadir("Howell1.csv"), DataFrame)

debs_path

Relative path using the StatisticalRethinking src/ directory.

Example to get access to the data subdirectory

debs_path("..", "data")

Note that in the projects, e.g. StatisticalRethinkingStan.jl and StatisticalRethinkingTuring.jl, the DrWatson approach is a better choice, i.e: sr_datadir(filename)