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

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  • Yanbing Zheng
  • Jun Zhu
  • Anindya Roy
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    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. Copyright 2010, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 97 (2010)
    Issue (Month): 1 ()
    Pages: 238-245

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    Handle: RePEc:oup:biomet:v:97:y:2010:i:1:p:238-245

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    Cited by:
    1. Martin Burda & Artem Prokhorov, 2013. "Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models," Working Papers tecipa-473, University of Toronto, Department of Economics.
    2. Zheng, Yanbing, 2011. "Shape restriction of the multi-dimensional Bernstein prior for density functions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 647-651, June.

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