Multiproposal Elliptical Slice Sampling

TL;DR

This paper presents Multiproposal Elliptical Slice Sampling, a novel self-tuning MCMC method that uses multiple proposals and a distance-informed acceptance criterion to improve mixing and efficiency in Bayesian inference with Gaussian priors.

Contribution

It generalizes existing elliptical slice sampling by enabling parallel proposals and a new acceptance mechanism, enhancing performance for high-dimensional problems.

Findings

Enables larger moves in state space for faster mixing.

Provides theoretical and experimental evidence of dimension-robust performance.

Achieves improved mixing with no additional computational cost for likelihood evaluations.

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.