Bayesian Methods
The following methods require DiffEqBayes.jl:
]add DiffEqBayes
using DiffEqBayes
stan_inference
stan_inference(prob::ODEProblem,t,data,priors = nothing;alg=:rk45,
num_samples=1000, num_warmups=1000, reltol=1e-3,
abstol=1e-6, maxiter=Int(1e5),likelihood=Normal,
vars=(StanODEData(),InverseGamma(2,3)))
stan_inference
uses Stan.jl to perform the Bayesian inference. The Stan installation process is required to use this function. t
is the array of time and data
is the array where the first dimension (columns) corresponds to the array of system values. priors
is an array of prior distributions for each parameter, specified via a Distributions.jl type. alg
is a choice between :rk45
and :bdf
, the two internal integrators of Stan. num_samples
is the number of samples to take per chain, and num_warmups
is the number of MCMC warmup steps. abstol
and reltol
are the keyword arguments for the internal integrator. likelihood
is the likelihood distribution to use with the arguments from vars
, and vars
is a tuple of priors for the distributions of the likelihood hyperparameters. The special value StanODEData()
in this tuple denotes the position that the ODE solution takes in the likelihood's parameter list.
turing_inference
function turing_inference(prob::DiffEqBase.DEProblem,alg,t,data,priors;
likelihood_dist_priors, likelihood, num_samples=1000,
sampler = Turing.NUTS(num_samples, 0.65), syms, kwargs...)
turing_inference
uses Turing.jl to perform its parameter inference. prob
can be any DEProblem
with a corresponding alg
choice. t
is the array of time points and data
is the set of observations for the differential equation system at time point t[i]
(or higher dimensional). priors
is an array of prior distributions for each parameter, specified via a Distributions.jl type. num_samples
is the number of samples per MCMC chain. The extra kwargs
are given to the internal differential equation solver.
dynamichmc_inference
dynamichmc_inference(prob::DEProblem,alg,t,data,priors,transformations;
σ = 0.01,ϵ=0.001,initial=Float64[])
dynamichmc_inference
uses DynamicHMC.jl to perform the bayesian parameter estimation. prob
can be any DEProblem
, data
is the set of observations for our model which is to be used in the Bayesian Inference process. priors
represent the choice of prior distributions for the parameters to be determined, passed as an array of Distributions.jl distributions. t
is the array of time points. transformations
is an array of Tranformations imposed for constraining the parameter values to specific domains. initial
values for the parameters can be passed, if not passed the means of the priors
are used. ϵ
can be used as a kwarg to pass the initial step size for the NUTS algorithm.
abc_inference
abc_inference(prob::DEProblem, alg, t, data, priors; ϵ=0.001,
distancefunction = euclidean, ABCalgorithm = ABCSMC, progress = false,
num_samples = 500, maxiterations = 10^5, kwargs...)
abc_inference
uses ApproxBayes.jl which uses Approximate Bayesian Computation (ABC) to perform its parameter inference. prob
can be any DEProblem
with a corresponding alg
choice. t
is the array of time points and data[:,i]
is the set of observations for the differential equation system at time point t[i]
(or higher dimensional). priors
is an array of prior distributions for each parameter, specified via a Distributions.jl type. num_samples
is the number of posterior samples. ϵ
is the target distance between the data and simulated data. distancefunction
is a distance metric specified from the Distances.jl package, the default is euclidean
. ABCalgorithm
is the ABC algorithm to use, options are ABCSMC
or ABCRejection
from ApproxBayes.jl, the default is the former which is more efficient. maxiterations
is the maximum number of iterations before the algorithm terminates. The extra kwargs
are given to the internal differential equation solver.