David B. Dunson 
Department of Statistical Science
Duke University
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“Wasserstein Posteriors: Robust and Scalable Bayes”
A general approach is proposed based on dividing data into subsets, drawing samples from each subset posterior via MCMC or another algorithm, and combining the resulting subset posterior measures. Combining relies on the geometric median or Barycenter of the subset posteriors, leading to massive improvements in computational times relative to running sampling on one machine. Theory support is provided and the approach is applied in a variety of settings.
