Visualizations for Assessing Convergence and Mixing of MCMC

Reference:

Jarkko Venna, Samuel Kaski, and Jaakko Peltonen. Visualizations for assessing convergence and mixing of MCMC. In N. Lavrac, D. Gamberger, H. Blockeel, and L. Todorovski, editors, Proceedings of ECML-2003, 14th European Conference on Machine Learning, pages 432–443, Berlin, 2003. Springer. Preprint postscript at http://www.cis.hut.fi/projects/mi/papers/ecml03.ps.gz.

Abstract:

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.

Suggested BibTeX entry:

@inproceedings{Venna03ecml,
    address = {Berlin},
    author = {Jarkko Venna and Samuel Kaski and Jaakko Peltonen},
    booktitle = {Proceedings of ECML-2003, 14th European Conference on Machine Learning},
    editor = {N. Lavrac and D. Gamberger and H. Blockeel and L. Todorovski},
    note = {Preprint postscript at \url{http://www.cis.hut.fi/projects/mi/papers/ecml03.ps.gz}},
    pages = {432-443},
    publisher = {Springer},
    title = {Visualizations for Assessing Convergence and Mixing of {MCMC}},
    year = {2003},
}