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 part of the state space might be a `poor' one for another part of the state space. We consider a component-wise multiple-try Metropolis (CMTM) algorithm that can automatically choose 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.
Cite
@article{arxiv.1603.03510,
title = {Adaptive Component-wise Multiple-Try Metropolis Sampling},
author = {Jinyoung Yang and Evgeny Levi and Radu V. Craiu and Jeffrey S. Rosenthal},
journal= {arXiv preprint arXiv:1603.03510},
year = {2017}
}