Efficient and Adaptive MCMC by Coupling Multiple Samples

• Activity Number: 339
• Type: Invited
• Date/Time: Wednesday, August 14, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing*
• Author(s): Gregory Warnes*+
• Affiliation(s): Pfizer Global R&D
• Keywords: Markov Chain Monte Carlo ; Bayesian Methods ; Parallel Computing ; Software ; Gibbs Sampling

Abstract

Hastings Coupling is a method of coupling a set of MCMC samples to enable sharing of information without disturbing the convergence properties of the individual chains. This information sharing allows algorithms that have improved efficiency, particularly in problems where mixing is difficult, such as multi-modal posterior distributions. We illustrate the Hastings Coupling method by presenting a particular case: the Normal Kernel Coupler (NKC).

The Normal Kernel Coupler (NKC) uses a normal kernel density estimator to create an estimate of the unknown target distribution using the set of current state vectors. At each iteration, one component state vector is updated using the current density estimate. We show that this sample is ergodic (irreducible, Harris recurrent, and aperiodic) for any continuous distribution on d-dimensional Euclidean space. In addition, simulation studies show that NKC outperforms standard MCMC methods on a variety of unimodal and bimodal problems.

The NKC is implemented as part of HYDRA, a general-purpose library for MCMC which provides a simple and extensible interface for performing MCMC on general problems.