Abstract - stat.columbia.edu

Stacking for Non-mixing bayesian ComputationsStacking for Non-mixing bayesian Computations:The Curse and Blessing of Multimodal PosteriorsYuling InstituteNew York, NY 10010, USAAki of Computer Science, Aalto University00076 Aalto, FinlandAndrew of Statistics and of Political Science, Columbia UniversityNew York, NY 10027, USAA bstractWhen working with multimodal bayesian posterior distributions, Markov chain MonteCarlo (MCMC) algorithms have difficulty moving between modes, and default variationalor mode-based approximate inferences will understate posterior uncertainty. And, even ifthe most important modes can be found, it is difficult to evaluate their relative weightsin the posterior. Here we propose an approach using parallel runs of MCMC, variational,or mode-based inference to hit as many modes or separated regions as possible and thencombine these using bayesian stacking, a scalable method for constructing a weightedaverage of distributions.

regression, horseshoe variable selection, and neural networks. Keywords: Bayesian stacking, Markov chain Monte Carlo, model misspeci cation, multimodal posterior, parallel computation, postprocessing. 1. Introduction Bayesian computation becomes di cult when posterior distributions are multimodal or

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  Selection, Variable, Bayesian, Variable selection

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