A method for efficiently sampling from distributions with correlated dimensions.

Abstract

Bayesian estimation has played a pivotal role in the understanding of individual differences. However, for many models in psychology, Bayesian estimation of model parameters can be difficult. One reason for this difficulty is that conventional sampling algorithms, such as Markov chain Monte Carlo (MCMC), can be inefficient and impractical when little is known about the target distribution--particularly the target distribution's covariance structure. In this article, we highlight some reasons for this inefficiency and advocate the use of a population MCMC algorithm, called differential evolution Markov chain Monte Carlo (DE-MCMC), as a means of efficient proposal generation. We demonstrate in a simulation study that the performance of the DE-MCMC algorithm is unaffected by the correlation of the target distribution, whereas conventional MCMC performs substantially worse as the correlation increases. We then show that the DE-MCMC algorithm can be used to efficiently fit a hierarchical version of the linear ballistic accumulator model to response time data, which has proven to be a difficult task when conventional MCMC is used.