Visualizations for Assessing Convergence and Mixing of MCMC
- Cite this paper as:
- Venna J., Kaski S., Peltonen J. (2003) Visualizations for Assessing Convergence and Mixing of MCMC. In: Lavrač N., Gamberger D., Blockeel H., Todorovski L. (eds) Machine Learning: ECML 2003. ECML 2003. Lecture Notes in Computer Science, vol 2837. Springer, Berlin, Heidelberg
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.
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