Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Kamatani, Kengo^1,2 

[1] Osaka Univ, Grad Sch Engn Sci, 1-3 Machikaneyama Cho, Toyonaka, Osaka 5608531, Japan

[2] Osaka Univ, Ctr Math Modeling & Data Sci, 1-3 Machikaneyama Cho, Toyonaka, Osaka 5608531, Japan

关键词: Markov chain;    Diffusion limit;    Consistency;    Monte Carlo;    Stein's method;   

DOI  :  10.1016/j.spa.2019.03.002

来源: Elsevier

【 摘 要 】

High-dimensional asymptotics of the random walk Metropolis Hastings algorithm are well understood for a class of light-tailed target distributions. Although this idealistic assumption is instructive, it may not always be appropriate, especially for complicated target distributions. We here study heavy-tailed target distributions for the random walk Metropolis algorithms. When the number of dimensions is d, the rate of consistency is d(2) and the calculation cost is O(d(3)), which might be too expensive in high dimension. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free