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Activity Number: 665 - Regression Methods for Longitudinal Data
Type: Contributed
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #305140 Presentation
Title: Posterior Contraction and Credible Sets for Filaments of Regression Functions
Author(s): Wei Li* and Subhashis Ghosal
Companies: Syracuse University and North Carolina State University
Keywords: Bayesian nonparametrics; nonparametric regression; credible sets; coverage; filaments; asymptotic theory

A filament consists of local maximizers of a smooth function when moving in a certain direction. Filamentary structures are important features of the shape of objects and considered as a useful lower dimensional characterization of multivariate data. There have been some recent theoretical studies of filaments in the nonparametric kernel density estimation context. We shall discuss a Bayesian approach to the filament estimation in regression context and present some results on posterior contraction rates obtained using a finite random B-splines series. Compared with the kernel-estimation method, the bias can be better controlled using the series method when the function is smoother, which allows obtaining better rates. In addition, we discuss a way to construct a credible set with sufficient frequentist coverage for the filaments and demonstrate the proposed method in simulations and one application to earthquake data.

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

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