Julia code supporting the paper:

Saifuddin Syed, Alexandre Bouchard-Côté, Kevin Chern, Arnaud Doucet (2026)
Journal of Royal Statistical Society, Series B 

Setup

Test with Julia 1.10.2 and CUDA runtime 12.5.

To setup:

using Pkg
Pkg.instantiate() 

To run a battery of test cases:

include("tests.jl")

Usage

Defining the reference and target (path)

To see an example of how to setup target distributions, see simple_mixture.jl. The main idea is that a custom struct is defined to hold the dataset, and dispatches are defined to specify target and reference.

The functions to dispatch are:

• iid_sample!(...) to sample from the reference,
• log_reference(...) to evaluate the log density of the reference,
• log_density_ratio(...) to evaluate the log of the un-normalized ratio between target and reference (e.g., in Bayesian models this is just the likelihood),
• dimensionality(...) to obtain the dimensionality of the latent space.

After doing so, create a variable say path and assign to it an instance of your custom struct. For example:

include("simple_mixture.jl")
backend = CPU() # or: CUDABackend()
path = SimpleMixture(backend) # since it holds data array, it needs to know if will be in CPU or GPU

Sampling

The interface for sampling is ais(...). The followoing methods are implemented:

• In sais.jl, we implement our SAIS (Sequential Annealed Importance Sampling) algorithm.
• In zha.jl, we implement Zhou et al (2016).

For example:

include("sais.jl")
a = ais(path, SAIS(10);
    N = 100, # number of particles
    backend,
    seed = 1)

Approximating expectation and estimating normalization constant

To approximate expectations:

∫(x -> x.^2, a.particles)

For the normalization constant:

a.particles.log_normalization

For ESS:

ess(a.particles)