PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Visualizations for assessing convergence and mixing of Markov chain Monte Carlo simulations
Jaakko Peltonen, Jarkko Venna and Samuel Kaski
Computational Statistics and Data Analysis 2009.

Abstract

Bayesian inference often requires approximating the posterior distribution by Markov chain Monte Carlo sampling. The samples come from the true distribution only after the simulation has converged, which makes detecting convergence a central problem. Commonly, several simulation chains are started from different points, and their overlap is used as a measure of convergence. Convergence measures cannot tell the cause of convergence problems; it is suggested that complementing them with proper visualization will help. A novel connection is pointed out: linear discriminant analysis (LDA) minimizes the overlap of the simulation chains measured by a common multivariate convergence measure. LDA is thus justified for visualizing convergence. However, LDA makes restrictive assumptions about the chains, which can be relaxed by a recent extension called discriminative component analysis (DCA). Lastly, methods are introduced for unidentifiable models and model families with variable number of parameters, where straightforward visualization in the parameter space is not feasible. NOTICE: this is the author's version of a work that was accepted for publication in Computational Statistics and Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright Elsevier B. V.

EPrint Type:Article
Additional Information:http://www.cis.hut.fi/projects/mi/abstracts/csda09.html
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:5433
Deposited By:Jaakko Peltonen
Deposited On:07 August 2009