juliaapproxinference/likelihoodfreeinference.jl

Likelihood-Free Inference for Julia.

LikelihoodfreeInference.jl

Given some measured data y0 and a potentially stochastic model model(x) that takes parameters x and returns simulated data y, LikelihoodfreeInference.jl allows to find approximate posterior distributions over x or approximate maximum likelihood (ML) and maximum a posteriori (MAP) point estimates, by runnning

run!(method, model, y0)

where method can be an Approximate Bayesian Computation (ABC) method PMC, AdaptiveSMC, K2ABC, KernelABC (subtypes(LikelihoodfreeInference.AbstractABC)) or PointEstimator, KernelRecursiveABC (subtypes(LikelihoodfreeInference.AbstractPointABC)).

Example

using LikelihoodfreeInference, StatsPlots, Distributions
model(x) = randn() .+ x
data = [2.]
method = KernelABC(delta = eps(),
                   K = 10^4,
                   kernel = Kernel(),
                   prior = TruncatedMultivariateNormal([0.], [5.],
                                                       lower = [-5.],
                                                       upper = [5.]))
result = run!(method, model, data)
println("Approximate posterior mean = $(mean(method))")
figure = histogram(method, normalize = true, xlims = (-5, 5))
plot!(figure, -1:.01:5, pdf.(Normal.(-1:.01:5, 26/25), 25/26*2.0))

See documentation or example notebooks Gaussian model and Blowfly model.