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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

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.

Suggested Citation

  • Yanbing Zheng & Jun Zhu & Anindya Roy, 2010. "Nonparametric Bayesian inference for the spectral density function of a random field," Biometrika, Biometrika Trust, vol. 97(1), pages 238-245.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:1:p:238-245
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    File URL: http://hdl.handle.net/10.1093/biomet/asp066
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    Cited by:

    1. repec:eee:stapro:v:128:y:2017:i:c:p:60-66 is not listed on IDEAS
    2. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.
    3. 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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