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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.
Monte Carlo sampler for a bimodal density mixes as poorly as a random-walk Metropolis sampler (Mangoubi et al., 2018). The extra challenge is that problems in sampling and modeling are confounded. Even if we can sample from truly multimodal distributions, the …
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