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 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.
Acknowledgements
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.
Citation
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
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