Case Studies in Bayesian Statistical Modelling and Analysis

24

Issues in Designing Hybrid Algorithms

Jeong E. Lee1¹, Kerrie L. Mengersen² and Christian P. Robert³

¹Auckland University of Technology, New Zealand

²Queensland University of Technology, Brisbane, Australia

³Université Paris-Dauphine, Paris, France and Centre de Recherche en Économie et Statistique (CREST), Paris, France

24.1 Introduction

In the Bayesian community, an ongoing imperative is to develop efficient algorithms for the more diverse and often complicated problems encountered in practice. There has been a substantial amount of progress on the fundamental ideas of designing efficient computational algorithms and the theoretical properties of these methods of simulation. The Markov chain Monte Carlo (MCMC) methods, originally proposed by Metropolis et al. (1953) and Hastings (1970), are designed to generate Markov chains with a given stationary distribution and various types of algorithms based on MCMC techniques have been proposed in the literature. Each algorithm has different strengths and weaknesses, and can be evaluated with respect to its ability to meet different criteria based on specified statistical properties. It is therefore natural that the question arises whether a better scheme can be developed by combining the best aspects of existing algorithms.

The concept of the hybrid algorithm was introduced by Tierney (1994). A hybrid algorithm can be designed from different perspectives, based on a variety of algorithms to combine and the way in which they are combined. ...