JSM 2011 Online Program

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Abstract Details

Activity Number: 156
Type: Topic Contributed
Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
Sponsor: International Chinese Statistical Association
Abstract - #301983
Title: Adaptive Smoothing with a Cauchy Process Prior
Author(s): Paul Speckman*+
Companies: University of Missouri at Columbia
Address: 134B Middlebush Bldg., Columbia, MO, 65211-6100,
Keywords: smoothing spline ; adaptive estimate ; Cauchy process
Abstract:

The equivalence between spline smoothing, which penalizes the $L_2$ norm of a derivative, and Bayesian inference with an integrated Brownian motion prior is well known. In this talk, we explore the use of Cauchy process in place of Gaussian process priors. For simplicity, we use a discrete approximation to the derivative, so that an exact, explicit solution exists. We demonstrate by example that the resulting Bayes estimator has many of the desirable properties of a penalized estimator with an $L_1$ penalty, for example. Moreover, fully Bayesian inference is easily obtained through efficient MCMC techniques. The prior can be extended to provide adaptive smoothing on a lattice in two dimensions. Illustrations with simulated and real data are provided.


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