Custom likelihood with Turing.jl

Specific Domains Probabilistic programming
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3

What you need to do is specify the lower and upper bounds of your parameters with your priors. I think you can simply use Uniform(lb, ub) in your use case. Here is a fairly straightforward example of specifying a custom likelihood distribution in Turing. Here is example code for running the linked model.

using Distributions, Turing, Random, Parameters
ProjDir = @__DIR__
cd(ProjDir)
include("LNR.jl")

@model model(data, Nr) = begin
    μ = Array{Real,1}(undef,Nr)
    μ ~ [Normal(0,3)]
    s ~ Uniform(0, pi/2)
    σ = tan(s)
    #σ ~ Truncated(Cauchy(0, 1), 0, Inf)
    for i in 1:length(data)
        data[i] ~ LNR(μ, σ, 0.0)
    end
end

Random.seed!(343)
Nreps = 50
error_count = fill(0.0, Nreps)
Nr = 3
Nobs = 10


μ = rand(Normal(0, 3), Nr)
σ = rand(Uniform(.2, 1))
dist = LNR(μ=μ, σ=σ, ϕ=0.0)
data = rand(dist, Nobs)
chain = sample(model(data, Nr), NUTS(1000, .8), 2000)