csda09

Jaakko Peltonen, Jarkko Venna, and Samuel Kaski. Visualizations for Assessing Convergence and Mixing of Markov Chain Monte Carlo Simulations. Computational Statistics and Data Analysis, 53, 4453-4470, 2009. (preprint pdf, final version on publisher pages)

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. A definitive version was subsequently published in Computational Statistics and Data Analysis, Volume 53, Issue 12, 1 October 2009, Pages 4453-4470, doi:10.1016/j.csda.2009.07.001

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The authors were supported by the Academy of Finland, decision numbers 108515 and 123983. This work was also supported in part by the IST Programme of the European Community, under the PASCAL2 Network of Excellence. This publication only reflects the authors' views.