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Activity Number: 134
Type: Contributed
Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract - #309282
Title: Convergence Assessment in Large Finite State Space MCMC with an Application to Bayesian Clustering
Author(s): Masoud Asgharian*+ and Ioana Ada Coxma and Vahid Partovi Nia
Companies: McGill University and University of Ottawa and École Polytechnique Montréal
Keywords: ayesian clustering ; Convergence assessment ; Gibbs sampling ; Markov chain Monte Carlo algorithm ; Regenerative simulation ; Split-merge algorithm

An alternative to the well-known method of agglomerative Bayesian clustering is consensus clustering, in which a Markov chain Monte Carlo (MCMC) sampling algorithm explores the finite space of cluster allocations. The implementation requires diagnostic tools for assessing convergence. While there has been a surge of articles on convergence diagnostic tools for continuous stationary distributions, Bayesian clustering has spawned demands for tools designed specifically for finite state spaces. In this article we fill this gap by proposing a quantitative convergence assessment criterion for MCMC algorithms on finite state spaces that has an intuitive interpretation as a test of hypothesis. We define a one-dimensional statistic of fit and derive its asymptotic distribution. The asymptotic variance is estimated by regenerative simulation, and we perform convergence assessment via a formal statistical significance test. Finally, we consider the particular application of clustering of genetic mutants of the flowering plant {\it Arabidopsis thaliana} via metabolic profiling.

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

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