Title :

Adaptive Component-wise Multiple-Try Metropolis Sampling

Resume :

One of the most widely used samplers in practice is the component-wise MetropolisHastings (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.

This is joint work with Evgeny Levi, Jinyoung Yang and Jeffrey Rosenthal.