June 2023 Spectral gaps and error estimates for infinite-dimensional Metropolis–Hastings with non-Gaussian priors
Bamdad Hosseini, James E. Johndrow
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Ann. Appl. Probab. 33(3): 1827-1873 (June 2023). DOI: 10.1214/22-AAP1854


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 Cesáro 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.


The authors are thankful to Prof. Andrew Stuart for interesting conversations regarding convergence properties of MCMC algorithms, and to Prof. Jonathan Mattingly for pointing out an error in an early draft of the manuscript. The authors are also grateful to the anonymous reviewers whose comments and suggestions helped us improve the article immensely.


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Bamdad Hosseini. James E. Johndrow. "Spectral gaps and error estimates for infinite-dimensional Metropolis–Hastings with non-Gaussian priors." Ann. Appl. Probab. 33 (3) 1827 - 1873, June 2023. https://doi.org/10.1214/22-AAP1854


Received: 1 May 2022; Published: June 2023
First available in Project Euclid: 2 May 2023

MathSciNet: MR4583659
zbMATH: 1515.65012
Digital Object Identifier: 10.1214/22-AAP1854

Primary: 60J05 , 62G99 , 62M40 , 65C05

Keywords: Bayesian inverse problem , Markov chain Monte Carlo , non-Gaussian , spectral gap , weak Harris’ theorem

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.33 • No. 3 • June 2023
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