A New Efficient MCMC Algorithm for Sampling Banana-Shaped Distributions Based on Coordinate Transformation

• Activity Number: 401
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Xiaodan Fan*+
• Companies: Chinese University of Hong Kong
• Keywords: Monte Carlo method ; Markov chain Monte Carlo ; banana-shaped distribution ; coordinate transformation ; effective sample size ; convergence rate

Abstract

When sampling from multivariate distributions whose density contours are banana-shaped due to due to the non-linear correlation structure, traditional Markov chain Monte Carlo (MCMC) methods suffer from severe low convergence. In this paper, a family of bivariate banana-shaped distributions is characterized. A new MCMC algorithm based on coordinate transformation is proposed to sample these complex distributions. The new algorithm is designed based on a parametric approximation of the target density function. A detailed comparison of the new method and existing methods, including adaptive importance sampling and the Riemannian Manifold Hybrid Monte Carlo algorithm, is performed using both benchmark examples and real data examples, which showed the advantage of the new method.