Mathematical Sciences - Statistics Seminar "Robust Bayesian inference via coarsening" by Jeff Miller (Harvard University) - Stratton Hall 304

Monday, March 12, 2018
11:00 am to 12:00 pm

Location

Floor/Room #: 
304

Statistics Seminar Series

Jeff Miller
Harvard University

Title: Robust Bayesian inference via coarsening

ABSTRACT:  The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class.  However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure, particularly when the data set is large.  We introduce a simple, coherent approach to Bayesian inference that improves robustness to small departures from the model: rather than conditioning on the observed data exactly, one conditions on the event that the model generates data close to the observed data, with respect to a given statistical distance.  When closeness is defined in terms of relative entropy, the resulting "coarsened posterior" can be approximated by simply raising the likelihood to a certain fractional power, making the method computationally efficient and easy to implement in practice.  We illustrate with real and simulated data, and provide theoretical results.

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