Striated Metropolis–Hastings sampler for high-dimensional models

Abstract

Having efficient and accurate samplers for simulating the posterior distribution is crucial for Bayesian analysis. We develop a generic posterior simulator called the “dynamic striated Metropolis–Hastings (DSMH)” sampler. Grounded in the Metropolis–Hastings algorithm, it pools the strengths from the equi-energy and sequential Monte Carlo samplers while avoiding the weaknesses of the standard Metropolis–Hastings algorithm and those of importance sampling. In particular, the DSMH sampler possesses the capacity to cope with extremely irregular distributions that contain winding ridges and multiple peaks; and it is robust to how the sampling procedure progresses across stages. The high-dimensional application studied in this paper provides a natural platform for testing any generic sampler.