The Multiple-Try Method and Local Optimization in Metropolis Sampling

Abstract

This article describes a new Metropolis-like transition rule, the multiple-try Metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling, we propose a novel method for incorporating local optimization steps into a MCMC sampler in continuous state-space. Numerical studies show that the new method performs significantly better than the traditional Metropolis-Hastings (M-H) sampler. With minor tailoring in using the rule, the multiple-try method can also be exploited to achieve the effect of a griddy Gibbs sampler without having to bear with griddy approximations, and the effect of a hit-and-run algorithm without having to figure out the required conditional distribution in a random direction.

Key Words:

• Adaptive direction sampling
• Conjugate gradient
• Damped sinusoidal
• Gibbs sampling
• Griddy Gibbs sampler
• Hit-and-run algorithm
• Markov chain Monte Carlo
• Metropolis algorithm
• Mixture model
• Orientational bias Monte Carlo.