Combining Principal Component Analysis with Parameter Line Searches to Construct Well-Designed Proposal Distributions for Metropolis-Hastings MCMC

• Activity Number: 461
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): David Andrew Kennedy*+ and Vanja Dukic and Greg Dwyer
• Companies: The University of Chicago and The University of Chicago and The University of Chicago
• Keywords: Metropolis-Hastings MCMC ; principal component analysis ; parallel computing ; within-host disease model

Abstract

When Markov-chain Monte Carlo (MCMC) is used to fit models to data, convergence times are limited by mixing rates and computational power. Here we present an adaptive MCMC algorithm, PCA-MCMC, suitable for highly parallel computing environments, and we use it to make inferences about a mechanistic model of the growth of virus populations inside insect hosts. The algorithm is initialized by parameter line-searches from which, a subset (4%) of parameter sets with the highest likelihood are subjected to principal component analysis (PCA). Next, multiple MCMC chains are run in parallel using normal proposals that approximate the distribution of principal components. Finally, the original parameter posterior density is obtained by back-transformation. Compared to a Metropolis-Hastings MCMC with untransformed parameters, PCA-MCMC had better mixing, shorter burn-in and faster convergence.