Work

Analysis of two-component Gibbs samplers using the theory of two projections

Year: 2024

Type: article

Abstract: The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix algebra exercises. It is found that in terms of asymptotic variance, the two-component random-scan Gibbs sampler is never much worse, and could be considerably better than its deterministic-scan counterpart, provided that the selection probability is appropriately chosen. This is especially the case when there is a large discrepancy in computation cost between the two components. The result contrasts with the known fact that the deterministic-scan version has a faster convergence rate, which can also be derived from the method herein. On the other hand, a modified version of the deterministic-scan sampler that accounts for computation cost can outperform the random-scan version.

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2066

Author: Qian Qin

Institution: University of Minnesota

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Large Sample Analysis of Markov Chain Monte Carlo Methods in Bayesian Statistics From a Frequentist Perspective