Multiproposal Elliptical Slice Sampling
Abstract
We introduce Multiproposal Elliptical Slice Sampling, a self-tuning multiproposal Markov chain Monte Carlo method for Bayesian inference with Gaussian priors. Our method generalizes the Elliptical Slice Sampling algorithm by 1) allowing multiple candidate proposals to be sampled in parallel at each self-tuning step, and 2) basing the acceptance step on a distance-informed transition matrix that can favor proposals far from the current state. This allows larger moves in state space and faster self-tuning, at essentially no additional wall clock time for expensive likelihoods, and results in improved mixing. We additionally provide theoretical arguments and experimental results suggesting dimension-robust mixing behavior, making the algorithm particularly well suited for Bayesian PDE inverse problems.
Cite
@article{arxiv.2602.22358,
title = {Multiproposal Elliptical Slice Sampling},
author = {Guillermina Senn and Nathan Glatt-Holtz and Giulia Carigi and Andrew Holbrook and Håkon Tjelmeland},
journal= {arXiv preprint arXiv:2602.22358},
year = {2026}
}