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

Zheng, Yanbing; Zhu, Jun

doi:10.1093/biomet/asp066

Cited by 26 publications

(15 citation statements)

References 22 publications

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“…For large data sets, it may even be possible to estimate the kernel function nonparametrically from the data. Zheng, Zhu and Roy (2010) and Reich and Fuentes (2012) use Bayesian nonparametrics to estimate the spatial covariance function of a Gaussian process. This approach could be extended to the extreme data, using, say, a Dirichlet process mixture prior for the kernel function.…”

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confidence: 99%

A hierarchical max-stable spatial model for extreme precipitation

Reich¹,

Shaby²

2012

Ann. Appl. Stat.

141

189

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Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence. We show that our specification of the random effect distribution leads to a max-stable process that has the popular Gaussian extreme value process (GEVP) as a limiting case. The proposed model is used to analyze the yearly maximum precipitation from a regional climate model.

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confidence: 99%

A hierarchical max-stable spatial model for extreme precipitation

Reich¹,

Shaby²

2012

Ann. Appl. Stat.

141

189

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“…Instead of restricting to a particular parametric model for the covariance function, Zheng et al (2010) and Reich and Fuentes (2012) treat the covariance function as an unknown to be estimated from the data. The standard approach for covariance modeling is to select a parametric covariance function .…”

Section: Bayesian Non-parametric Priors For a Covariance Functionmentioning

confidence: 99%

Nonparametric Bayesian Inference in Biostatistics

Mitra

Müeller²

2015

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We briefly review some of the nonparametric Bayesians models that are most widely used in biostatistics and bioinformatics. We define the Dirichlet process, Dirichlet process mixtures, the Polya tree, the dependent Dirichlet process and the Gaussian process prior. These few models and variations cover a major part of the models that are used in the literature. The discussion includes references to variations of the basic models that are defined in the chapters of this volume.

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“…The number of mixture components is a smoothing parameter, chosen to have a discrete prior. Zheng et al (2010) generalized this and constructed a multi-dimensional Bernstein polynomial prior to estimate the spectral density function of a random field. Also extending the work of Choudhuri et al (2004), Macaro (2010) used informative priors to extract unobserved spectral components in a time series, and Macaro and Prado (2014) generalized this to multiple time series.…”

Section: Introductionmentioning

confidence: 99%

Bayesian nonparametric spectral density estimation using B-spline priors

2018

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We present a new Bayesian nonparametric approach to estimating the spectral density of a stationary time series. A nonparametric prior based on a mixture of B-spline distributions is specified and can be regarded as a generalization of the Bernstein polynomial prior of Petrone (1999a,b) and Choudhuri et al. (2004). Whittle's likelihood approximation is used to obtain the pseudo-posterior distribution. This method allows for a data-driven choice of the number of mixture components and the location of knots. Posterior samples are obtained using a Metropolis-within-Gibbs Markov chain Monte Carlo algorithm, and mixing is improved using parallel tempering. We conduct a simulation study to demonstrate that for complicated spectral densities, the B-spline prior provides more accurate Monte Carlo estimates in terms of L 1 -error and uniform coverage probabilities than the Bernstein polynomial prior. We apply the algorithm to annual mean sunspot data to estimate the solar cycle. Finally, we demonstrate the algorithm's ability to estimate a spectral density with sharp features, using real gravitational wave detector data from LIGO's sixth science run, recoloured to match the Advanced LIGO target sensitivity.

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

Cited by 26 publications

References 22 publications

A hierarchical max-stable spatial model for extreme precipitation

A hierarchical max-stable spatial model for extreme precipitation

Nonparametric Bayesian Inference in Biostatistics

Bayesian nonparametric spectral density estimation using B-spline priors

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