Spectral gaps and error estimates for infinite-dimensional Metropolis-Hastings with non-Gaussian priors

TL;DR

This paper analyzes a class of Metropolis-Hastings algorithms for non-Gaussian priors in Banach spaces, establishing spectral gaps and error bounds for approximations, with broad applicability to various likelihoods and prior perturbations.

Contribution

It introduces spectral gap results and error estimates for infinite-dimensional Metropolis-Hastings algorithms with non-Gaussian priors, expanding theoretical understanding and practical bounds.

Findings

Spectral gap established in a Wasserstein-like semimetric.

Error bounds provided for algorithm approximations.

Applicability demonstrated across diverse prior and likelihood perturbations.

Abstract

We study a class of Metropolis-Hastings algorithms for target measures that are absolutely continuous with respect to a large class of non-Gaussian prior measures on Banach spaces. The algorithm is shown to have a spectral gap in a Wasserstein-like semimetric weighted by a Lyapunov function. A number of error bounds are given for computationally tractable approximations of the algorithm including bounds on the closeness of Ces\'aro averages and other pathwise quantities via perturbation theory. Several applications illustrate the breadth of problems to which the results apply such as various likelihood approximations and perturbations of prior measures.