Visualizations for Assessing Convergence and Mixing of MCMC
Bayesian inference often requires approximating the posterior distribution with Markov Chain Monte Carlo (MCMC) sampling. A central problem with MCMC is how to detect whether the simulation has converged. The samples come from the true posterior distribution only after convergence. A common solution is to start several simulations from different starting points, and measure overlap of the different chains. We point out that Linear Discriminant Analysis (LDA) minimizes the overlap measured by the usual multivariate overlap measure. Hence, LDA is a justified method for visualizing convergence. However, LDA makes restrictive assumptions about the distributions of the chains and their relationships. These restrictions can be relaxed by a recently introduced extension.
Unable to display preview. Download preview PDF.
- 1.Gilks, W.R., Richardson, S., Spiegelhalter, D.J.: Markov Chain Monte Carlo in Practice. Interdisciplinary Statistics, Chapman & Hall/CRC, Boca Raton, Florida (1995)Google Scholar
- 2.Brooks, S., Gelman, A.: Some issues in monitoring convergence of iterative simulations. In: Proceedings of the Section on Statistical Computing. ASA (1998)Google Scholar
- 8.Kaski, S., Peltonen, J.: Informative Discriminant Analysis. In: Proceedings of ICML 2003, The Twentieth International Conference on Machine Learning (2003) (in press)Google Scholar
- 9.Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Texts in Statistical Science. Chapman & Hall/CRC, Boca Raton, Florida (1995)Google Scholar
- 10.Theodoridis, S., Koutroumbas, K.: Pattern Recognition. Academic Press, San Diego (1999)Google Scholar