Open Access
November 2019 Consistent estimation of the spectrum of trace class Data Augmentation algorithms
Saptarshi Chakraborty, Kshitij Khare
Bernoulli 25(4B): 3832-3863 (November 2019). DOI: 10.3150/19-BEJ1112


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.


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Saptarshi Chakraborty. Kshitij Khare. "Consistent estimation of the spectrum of trace class Data Augmentation algorithms." Bernoulli 25 (4B) 3832 - 3863, November 2019.


Received: 1 November 2017; Revised: 1 July 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110157
MathSciNet: MR4010974
Digital Object Identifier: 10.3150/19-BEJ1112

Keywords: Data Augmentation algorithms , eigenvalues of Markov operators , MCMC convergence , trace class Markov operators

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 4B • November 2019
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