2018/09/30 by Bamdad Hosseini, Hosseini, Bamdad, James E. Johndrow +2
Computer Science · Mathematics · #60J05 #62G99 #62M40 #65C05 #Applied mathematics #Approximations of π #Artificial intelligence #Bayesian probability #Class (philosophy) #Closeness #Computer science #FOS: Mathematics #Gaussian #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Mathematical analysis #Mathematics #Prior probability #Probability (math.PR) #Statistics #Statistics Theory (math.ST) #Topological and Geometric Data Analysis #math.PR #math.ST #msc:60J05 #msc:62G99 #msc:62M40 #msc:65C05 #stat.TH
paper · pdf · doi:10.48550/arxiv.1810.00297
openalex publication_date 2018/09/30 · arxiv created 2022/05/17 · arxiv updated 2022/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.