Mixing time of an unaligned Gibbs sampler on the square

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Gerencser, Balazs^1,2 

[1] MTA Alfred Renyi Inst Math, Redltanoda Utca 13-15, H-1053 Budapest, Hungary

[2] Eotvos Lorand Univ, Dept Probabil Theory & Stat, Pazmany Peter Setany 1-C, H-1117 Budapest, Hungary

关键词: Gibbs sampler;    Markov chain;    Mixing time;   

DOI  :  10.1016/j.spa.2018.10.004

来源: Elsevier

【 摘 要 】

The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square [0, 1](2) to approach a stationary distribution with density proportional to exp(-A(2)(u - v)(2)) for (u, v) is an element of [0, 1](2) with some large parameter A. Diaconis conjectured the mixing time of this process to be O(A(2)) which we confirm in this paper. This improves on the currently known O(exp(A(2))) estimate. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free