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Activity Number: 139
Type: Contributed
Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract #321289 View Presentation
Title: Bayesian Estimation of Heavy-Tailed Densities Using Transformations
Author(s): Andrew Bean* and Xinyi Xu and Steven N. MacEachern
Companies: The Ohio State University and The Ohio State University and The Ohio State University
Keywords: density estimation ; transformations ; convergence rates ; heavy tailed densities ; Dirichlet process

Recently, several authors studying the asymptotic performance of nonparametric Bayesian models for density estimation have succeeded in establishing fast posterior contraction rates that mimic frequentist rates, yet most of these authors' results require the true density to have exponentially decaying tails or compact support. In this paper we show that by incorporating a tail-correcting transformation of the sample and modeling the transformed density using a Dirichlet process mixture, the same fast rates can be obtained for a much broader class of densities, including those with polynomially decaying tails. Empirical evidence is given for the effectiveness of the transformation method, including an analysis of a heavy-tailed sample of body mass index (BMI) observations for a large survey of Ohio adults.

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

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