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Biometrika

Year: 2010  |  Volume: 97  |  Issue: 1  |  Page No.: 238 - 245

Nonparametric Bayesian inference for the spectral density function of a random field

Y Zheng, J Zhu and A. Roy

Abstract

A powerful technique for inference concerning spatial dependence in a random field is to use spectral methods based on frequency domain analysis. Here we develop a nonparametric Bayesian approach to statistical inference for the spectral density of a random field. We construct a multi-dimensional Bernstein polynomial prior for the spectral density and devise a Markov chain Monte Carlo algorithm to simulate from the posterior of the spectral density. The posterior sampling enables us to obtain a smoothed estimate of the spectral density as well as credible bands at desired levels. Simulation shows that our proposed method is more robust than a parametric approach. For illustration, we analyse a soil data example.

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