Journal
STATISTICS AND COMPUTING
Volume 25, Issue 4, Pages 809-819Publisher
SPRINGER
DOI: 10.1007/s11222-015-9563-8
Keywords
Bayesian computation; Highest posterior density; Bootstrap
Funding
- National Science Foundation [CNS-1205516]
- Institute of Education Sciences [DE R305D140059]
- Department of Energy [DE-SC0002099]
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Bayesian highest posterior density (HPD) intervals can be estimated directly from simulations via empirical shortest intervals. Unfortunately, these can be noisy (that is, have a high Monte Carlo error). We derive an optimal weighting strategy using bootstrap and quadratic programming to obtain a more computationally stable HPD, or in general, shortest probability interval (Spin). We prove the consistency of our method. Simulation studies on a range of theoretical and real-data examples, some with symmetric and some with asymmetric posterior densities, show that intervals constructed using Spin have better coverage (relative to the posterior distribution) and lower Monte Carlo error than empirical shortest intervals. We implement the new method in an R package (SPIn) so it can be routinely used in post-processing of Bayesian simulations.
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