The development of a convergence diagnostic for Markov Chain Monte Carlo estimation

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Matthew Joseph Burke (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Advisor
Robert Henson

Abstract: The development and investigation of a convergence diagnostic for Markov Chain Monte Carlo (MCMC) posterior distributions is presented in this paper. The current method is an adaptation of an existing convergence diagnostic based on the Cumulative Sum (CUSUM, Page 1954; Yu & Mykland, 1998; Brooks, 1998c) procedure. The diagnostic under development is seen to be an improvement over the technique upon which it is based because it offers a simple way to remove one of the two major assumptions made by the previous method, namely that the shape of the distribution under consideration is symmetric. Results are mixed, but there is some evidence to indicate that the new technique is sensitive to the degree of autocorrelation present and the stability of the chains. Also, the new diagnostic behaves differently than three existing convergence diagnostics.

Additional Information

Publication
Dissertation
Language: English
Date: 2011
Keywords
Convergence Diagnostic, Markov Chain Monte Carlo
Subjects
Markov processes $x Numerical solutions
CUSUM technique
Convergence
Monte Carlo method