Online Program Home
My Program

Abstract Details

Activity Number: 589 - Topics in Data Mining, Forecasting, and Bayesian Inference for National Security
Type: Contributed
Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics in Defense and National Security
Abstract #329517
Title: Consistent Estimation of the Spectrum of Trace Class Data Augmentation Algorithms
Author(s): Saptarshi Chakraborty* and Kshitij Khare
Companies: University of Florida and University of Florida
Keywords: MCMC; eigenvalues; trace class; Data Augmentation

Markov chain Monte Carlo is widely used in a variety of scientific applications to generate approximate samples from intractable distributions. A thorough understanding of the convergence and mixing properties of these Markov chains can be obtained by studying the spectrum of the associated Markov operator. While several methods to bound/estimate the second largest eigenvalue are available in the literature, very few general techniques for consistent estimation of the entire spectrum have been proposed. Existing methods for this purpose require the Markov transition density to be available in closed form, which is often not true in practice, especially in modern statistical applications. In this paper, we propose a novel method to consistently estimate the entire spectrum of a general class of Markov chains arising from a popular and widely used statistical approach known as Data Augmentation. The transition densities of these Markov chains can often only be expressed as intractable integrals. We illustrate the applicability of our method using real and simulated data.

Authors who are presenting talks have a * after their name.

Back to the full JSM 2018 program