Analysis of two-component Gibbs samplers using the theory of two projections
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.
Keywords
Cite
@article{arxiv.2201.12500,
title = {Analysis of two-component Gibbs samplers using the theory of two projections},
author = {Qian Qin},
journal= {arXiv preprint arXiv:2201.12500},
year = {2024}
}