New methods for mode jumping in Markov chain Monte Carlo algorithms

Abstract

Standard Markov chain Monte Carlo (MCMC) sampling methods can experience problem sampling from multi-modal distributions. A variety of sampling methods have been introduced to overcome this problem. The mode jumping method of Tjelmeland & Hegstad (2001) tries to find a mode and propose a value from that mode in each mode jumping attempt. This approach is inefficient in that the work needed to find each mode and model the distribution in a neighbourhood of the mode is carried out repeatedly during the sampling process. We shall propose a new mode jumping approach which retains features of the Tjelmeland & Hegstad (2001) method but differs in that it finds the modes in an initial search, then uses this information to jump between modes effectively in the sampling run. Although this approach does not allow a second chance to find modes in the sampling run, we can show that the overall probability of missing a mode in our approach is still low. We apply our methods to sample from distributions which have continuous variables, discrete variables, a mixture of discrete and continuous variables and variable dimension. We show that our methods work well in each case and in general, are better than the MCMC sampling methods commonly used in these cases and also, are better than the Tjelmeland & Hegstad (2001) method in particular.

Date of Award	1 Mar 2009
Original language	English
Awarding Institution	University of Bath
Supervisor	Christopher Jennison (Supervisor)