Adaptive Component-Wise Multiple-Try Metropolis Sampling

ABSTRACT

One of the most widely used samplers in practice is the component-wise Metropolis–Hastings (CMH) sampler that updates in turn the components of a vector-valued Markov chain using accept–reject moves generated from a proposal distribution. When the target distribution of a Markov chain is irregularly shaped, a “good” proposal distribution for one region of the state–space might be a “poor” one for another region. We consider a component-wise multiple-try Metropolis (CMTM) algorithm that chooses from a set of candidate moves sampled from different distributions. The computational efficiency is increased using an adaptation rule for the CMTM algorithm that dynamically builds a better set of proposal distributions as the Markov chain runs. The ergodicity of the adaptive chain is demonstrated theoretically. The performance is studied via simulations and real data examples. Supplementary material for this article is available online.

KEYWORDS:

• Adaptive Markov chain Monte Carlo
• Component-wise Metropolis–Hastings
• Multiple-try Metropolis

Acknowledgments

The authors thank the editor, the associate editor, and three anonymous referees for thorough comments and insightful suggestions that have greatly improved the article.

Funding

Funding support for this work was provided by individual grants to RVC and JSR from the Natural Sciences and Engineering Research Council of Canada.