Locally Adaptive Markov Chain Monte Carlo

• Activity Number: 417
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Anthony Lee*+ and Christophe Andrieu and Arnaud Doucet
• Companies: University of Warwick and University of Bristol and University of Oxford
• Keywords: Markov chain Monte Carlo ; Auxiliary variables ; Sequential Monte Carlo

Abstract

The use of auxiliary variables in various Monte Carlo methods has proliferated both explicitly and implicitly over the last two decades, as our understanding of how to devise effective algorithms has grown. In addition, massively parallel 'many-core' processors have become the focus of the high performance computing community for a variety of physical reasons, providing a strong incentive for algorithms in computational statistics to exhibit specific types of parallelism. Within the field of Monte Carlo methodology, population-based methods such as sequential Monte Carlo and pseudo-marginal methods can make use of available parallel resources while allowing advantageous, principled interaction of random variables. A perspective on auxiliary variables within reversible Markov chain Monte Carlo (MCMC) kernels that allows for the flexible construction of population-based MCMC kernels is described. One opportunity the methodology presents is the "local adaptation" of MCMC kernels with a given equilibrium distribution, in that some aspects of the kernels are automatically adapted to the target distribution of interest. Such kernels hold some promise in a variety of applications.