Abstract:
*Joint work with David Dunson and Cheng Li, both from Duke University.
For further details, see the manuscript: http://arxiv.org/abs/1508.05880v1

The promise of Bayesian methods for big data sets has not fully been realized due to the lack of scalable computation-al algorithms. For massive data, it is necessary to store and process subsets on different machines in a distributed man-ner. We propose a simple, general, and highly efficient ap-proach, which first runs a posterior sampling algorithm in parallel on different machines for subsets of a large data set. To combine these subset posteriors, we calculate the Wasserstein barycenter via a highly efficient linear pro-gram. The resulting estimate for the Wasserstein posterior (WASP) has an atomic form, facilitating straightforward estimation of posterior summaries of functionals of inter-est. The WASP approach allows posterior sampling algo-rithms for smaller data sets to be trivially scaled to huge da-ta. We provide theoretical justification in terms of posterior consistency and algorithm efficiency. Examples are provid-ed in complex settings including Gaussian process regres-sion and nonparametric Bayes mixture models.

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