Journal
BIOMETRIKA
Volume 104, Issue 3, Pages 665-680Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asx033
Keywords
Credible interval; Markov chain Monte Carlo; Quantile estimation; Wasserstein barycentre
Funding
- United States National Science Foundation
- Office of Naval Research
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Standard posterior sampling algorithms, such as Markov chain Monte Carlo procedures, face major challenges in scaling up to massive datasets. We propose a simple and general posterior interval estimation algorithm to rapidly and accurately estimate quantiles of the posterior distributions for one-dimensional functionals. Our algorithm runs Markov chain Monte Carlo in parallel for subsets of the data, and then averages quantiles estimated from each subset. We provide strong theoretical guarantees and show that the credible intervals from our algorithm asymptotically approximate those from the full posterior in the leading parametric order. Our algorithm has a better balance of accuracy and efficiency than its competitors across a variety of simulations and a real-data example.
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