The Polya Tree Sampler: Towards Efficient and Automatic Independent Metropolis Proposals

• Activity Number: 303
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Alejandro Jara*+ and Timothy Edward Hanson and Joao Monteiro
• Companies: Pontificia Universidad Católica de Chile and University of Minnesota and University of Minnesota
• Keywords: Adaptive MCMC ; Metropolis-Hastings ; Density Approximation ; Polya trees

Abstract

We present a simple, efficient, and computationally cheap sampling method for exploring an unnormalized multivariate density, such as a posterior density, called the Polya tree sampler. The algorithm constructs an independent proposal based on an approximation of the target density which is built from a set of (initial) support points and the predictive density of a finite multivariate Polya tree. In an initial warming-up phase, the support points are iteratively relocated to regions of higher support under the target distribution to minimize the distance between the target distribution and the Polya tree predictive distribution. In the sampling phase, samples from the final approximating mixture of finite Polya trees are used as candidates which are accepted with a standard Metropolis-Hastings acceptance probability. ** A. Jara's research is supported by Fondecyt grant 3095003