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Activity Number: 625 - Modern Non-Parametrics
Type: Invited
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #300234 Presentation
Title: Coverage of Bayesian Credible Sets for Monotone Regression
Author(s): Subhashis Ghoshal* and Moumita Chakraborty
Companies: North Carolina State University and North Carolina State University
Keywords: Monotone regression; isotonization; credible set; coverage; projection posterior

We adopt a Bayesian approach to univariate nonparametric regression under a monotonicity constraint. We put a prior distribution on the regression function through step functions. We first disregard the monotonicity constraint and put conjugate normal prior on the step heights and obtain the corresponding posterior distribution. We then construct a "projection posterior distribution" by isotonizing posterior samples of step-heights, which contracts optimally. The projection posterior is also easier to compute and easier to analyze theoretically compared with a traditional posterior distribution based on a prior with the monotonicity constraint. We obtain the asymptotic frequentist coverages of posterior credible intervals of function values at given points and observe that the asymptotic coverages exceed the nominal credibility levels. This is the exact opposite of a phenomenon observed by Cox for coverage of credible sets for smooth functions. We also show that a targeted coverage can be achieved by resetting the credibility appropriately.

Authors who are presenting talks have a * after their name.

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