Activity Number:

260
 SPEED: Topics in Bayesian Analysis

Type:

Contributed

Date/Time:

Monday, July 30, 2018 : 3:05 PM to 3:50 PM

Sponsor:

Section on Bayesian Statistical Science

Abstract #332605


Title:

A Theoretical Framework for Bayesian Nonparametric Regression: Orthonormal Random Series and Rates of Contraction

Author(s):

Fangzheng Xie* and Wei Jin and Yanxun Xu

Companies:

Johns Hopkins University and Johns Hopkins University and Johns Hopkins University

Keywords:

Bayesian nonparametric regression;
integrated L2distance;
orthonormal random series;
rate of contraction

Abstract:

We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated L2distance without assuming the regression function space to be uniformly bounded. The framework is built upon orthonormal random series in a flexible manner. A general theorem for deriving rates of contraction for Bayesian nonparametric regression is provided under the proposed framework. As specific applications, we obtain the nearparametric rate of contraction for the squaredexponential Gaussian process when the true function is analytic, the adaptive rates of contraction for the sieve prior, and the adaptiveandexact rates of contraction for the unmodified block prior when the true function is alphasmooth. Extensions to wavelet series priors and fixeddesign regression problems are also discussed.
