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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.1214/22-aap1854

Bamdad Hosseini, James E Johndrow

引用次数: 1

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.

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具有非高斯先验的无限维Metropolis-Hastings的谱隙和误差估计

研究了一类针对Banach空间上一大类非高斯先验测度绝对连续的目标测度的Metropolis-Hastings算法。该算法在由Lyapunov函数加权的类wasserstein半度量中具有谱间隙。通过摄动理论给出了该算法计算上易于处理的近似的一些误差界限，包括Cesáro平均值和其他路径量的接近界限。几个应用说明了结果适用的问题的广度，例如各种似然近似和先前测量的扰动。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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