Bayesian Analysis

Bayesian estimation of intensity surfaces on the sphere via needlet shrinkage and selection

James G. Scott

Full-text: Open access

Abstract

This paper describes an approach for Bayesian modeling in spherical data sets. Our method is based upon a recent construction called the needlet, which is a particular form of spherical wavelet with many favorable statistical and computational properties. We perform shrinkage and selection of needlet coefficients, focusing on two main alternatives: empirical-Bayes thresholding, and Bayesian local shrinkage rules. We study the performance of the proposed methodology both on simulated data and on two real data sets: one involving the cosmic microwave background radiation, and one involving the reconstruction of a global news intensity surface inferred from published Reuters articles in August, 1996. The fully Bayesian approach based on robust, sparse shrinkage priors seems to outperform other alternatives.

Article information

Source
Bayesian Anal. Volume 6, Number 2 (2011), 307-327.

Dates
First available in Project Euclid: 13 June 2012

Permanent link to this document
http://projecteuclid.org/euclid.ba/1339612048

Digital Object Identifier
doi:10.1214/11-BA611

Mathematical Reviews number (MathSciNet)
MR2806246

Zentralblatt MATH identifier
1330.62221

Subjects
Primary: 62H11: Directional data; spatial statistics
Secondary: 42C40: Wavelets and other special systems 62F15: Bayesian inference 62H12: Estimation 62J07: Ridge regression; shrinkage estimators 62M40: Random fields; image analysis 62P25: Applications to social sciences

Keywords
needlets shrinkage estimate spherical wavelets

Citation

Scott, James G. Bayesian estimation of intensity surfaces on the sphere via needlet shrinkage and selection. Bayesian Anal. 6 (2011), no. 2, 307--327. doi:10.1214/11-BA611. http://projecteuclid.org/euclid.ba/1339612048.


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