Regeneration-Based Adaptation for Variable-at-a-Time MCMC

• Activity Number: 558
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Ronald Neath*+
• Companies: Hunter College
• Keywords: Markov chain Monte Carlo ; Adaptive MCMC ; Regenerative simulation

Abstract

Adaptive Markov chain Monte Carlo (MCMC) is a Markov chain simulation technique in which the Markov transition kernel is periodically updated to reflect information about the target distribution contained in previous draws. Gilks, Roberts and Sahu (1998) proposed an adaptive MCMC algorithm based on the method of regenerative simulation and proved that, provided each tour begins at a regeneration with respect to the adapted transition kernel, ergodic averages are consistent, and asymptotically valid standard errors are available. Further, allowing the chain to adapt only at regeneration times obviates the need to assume adaptation probability goes to zero, as required for most adaptive MCMC algorithms. In this talk we extend the work of Gilks et al. to develop a regeneration-based adaptation scheme for variable-at-a-time Metropolis-Hastings algorithms (aka Metropolised Gibbs samplers). Our method is illustrated in a pair of examples.