metropolis.jl

abstract type RejectionBasedSampler <: AbstractSampler end

struct MetropolisHastings{P <: AbstractProposal} <: RejectionBasedSampler
    proposal :: P
end 

function AbstractMCMC.step(rng::AbstractRNG, model::AbstractModel, sampler::MetropolisHastings; kwargs...)
    x   = rand(rng, sampler.proposal)
    f_x = logdensity(model, x)
    return (true, x, f_x), (x, f_x)
end
function AbstractMCMC.step(rng::AbstractRNG, model::AbstractModel, sampler::MetropolisHastings, state; kwargs...)
    x, f_x = state
    y = propose(rng, sampler.proposal, x)
    f_y = logdensity(model, y)
    q = logpratio(sampler.proposal, x, y)
    A = min( f_y - f_x + q, 0)
    accept = log(rand(rng)) < A
    if accept 
        return (true, y, f_y), (y, f_y)
    else
        return (false, x, f_x), (x, f_x)
    end
end