AdaptEllipticalSliceSampler.jl

This package contains a Julia implementation of adaptive generalized elliptical slice sampling. Adaptive generalized elliptical sliced sampling (AGESS) facilitates Bayesian computation on a wide variety of (lower semi-continuous) target distributions. Specifically, we have illustrated the utility of AGESS across target distributions that are non-differentiable, non-elliptical, multi-modal, high-dimensional, and/or are constrained to an open subset of $\mathbb{R}^{P}$. Using AGESS to sample from the posterior of your own models is relatively simple and can be broken down into the following steps:

1. Install Julia and the AdaptEllipticalSliceSampler.jl package (See Installation page)
2. Write a Julia function that efficiently evaluates the log posterior density (See Performance Tips and Tutorials pages)
3. Call the AGESS function (See Tutorials pages)

Usage with Turing.jl

As of v0.2.0, AdaptEllipticalSliceSampler.jl implements the AbstractMCMC.jl interface, so AGESS can be used as an external sampler for any Turing.jl model:

using Turing, AdaptEllipticalSliceSampler

## Linear Regression using Turing.jl
@model function linear_regression(X, y)
    P = size(X, 2)
    σ² ~ InverseGamma(1, 1)
    β ~ MvNormal(zeros(P), I)
    y ~ MvNormal(X * β, σ² * I)
end

## Generate some example data
N, P = 1000, 10
X = randn(N, P)
β_true = randn(P)
y = X * β_true + randn(N) * 0.5

## Run MCMC
n_MCMC = 10_000
model = linear_regression(X, y)
sampler = AGESSSampler(model, n_MCMC)
chain = sample(model, sampler, n_MCMC)

Breaking change (v0.2.0): AGESS_single_step! and AGESS_single_step_1d! now require an explicit rng argument and take separate x_prev/x_new vectors instead of a shared matrix and index. If you're using these lower-level functions directly, see the Factor Models tutorial for the updated usage.

New in v0.3.0: Block Updates and Resuming Chains

For models with structure – e.g. a hierarchical model where a parameter's likelihood only depends on a subset of the data – AGESSSampler (and AGESS) now accept a blocks keyword that lets you supply a cheaper conditional log-density for a block of coordinates, instead of always evaluating the full log_posterior on every 1-d update. See the Performance Tips page for an example.

Long-running chains can also be resumed: sample(...; save_state = true) saves the final sampler state on the returned chain, and it is retrievable via AGESS_loadstate. The last state is then passed into initial_state to continue sampling from exactly where a previous run left off (see example below).

## using chain as defined above
chain2 = sample(model, sampler, n_MCMC; initial_state = AGESS_loadstate(chain))
chain_combined = vcat(chain, chain2)

References

If you found this package useful in your own work and want to cite it in a paper, please consider using the following suggested citation:

N. Marco and S. T. Tokdar. Adaptive generalized elliptical slice sampling. arXiv preprint arXiv:2605.21659, 2026.

Link to Paper.