Toward HPD Regions from MCMC Samples

• Activity Number: 575
• Type: Invited
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Robert L Wolpert*+
• Companies: Duke University
• Keywords: HPD ; Posterior

Abstract

Many physicists like to think about uncertainty in data and models in a different way than most statisticians do--- they regard the evidence from experiments as a "confinement" of parameter values, a separation of the parameter space into one (hopefully small) region in which the "true" parameter value might lie, and its complement whose values are untenable in light of the experiment. It is hoped that identifying and visualizing the boundary of the tenable region may lead to further physical insight and suggest ways to improve existing physical models. In support of this perspective, we are developing methods intended to identify approximate "highest posterior density" or "hpd" regions of parameter space from MCMC output streams.

For one-dimensional parameter spaces this is a well-understood problem solved in 1999 by Ming-Hui Chen and Qi-Man Shao. In two or more dimensions the problem is more delicate.

As a step toward finding suitable approximate HPD regions, we generate convex polygons in the plane and polyhedra in higher dimensions and mount a stochastic search for the smallest-volume polygons containing a prescribed fraction of the MCMC points.