SPECTRAL GAPS AND ERROR ESTIMATES FOR INFINITE-DIMENSIONAL METROPOLIS-HASTINGS WITH NON-GAUSSIAN PRIORS

• 成果类型: Article
• 署名作者: Hosseini, Bamdad; Johndrow, James E.
• 署名单位: University of Washington; University of Washington Seattle; University of Pennsylvania
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1854
• 发表日期: 2023
• 页码: 1827-1873
• 关键词: Bayesian Inverse Problems; Uncertainty Quantification; LIMIT-THEOREMS; CONVERGENCE; algorithms; rates

摘要

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 spec-tral gap in a Wasserstein-like semimetric weighted by a Lyapunov function. A number of error bounds are given for computationally tractable approxima-tions of the algorithm including bounds on the closeness of Cesaro averages and other pathwise quantities via perturbation theory. Several applications il-lustrate the breadth of problems to which the results apply such as various likelihood approximations and perturbations of prior measures.