The multiple-try method and local optimization in metropolis sampling

This article describes a new Metropolis-like transition rule, the multiple- try Metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using t his transition rule together with adaptive direction sampling. we propose a novel method for incorporating local optimization steps into a MCMC sample r in continuous state-space. Numerical studies show that the new method per forms significantly better than the traditional Metropolis-Hastings (M-H) s ampler. 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 distributio n in a random direction.