Empirical Bayes spatial prediction using a Monte Carlo EM algorithm

Khaledi, Majid Jafari; Rivaz, Firoozeh

doi:10.1007/s10260-007-0081-5

Cited by 9 publications

(7 citation statements)

References 19 publications

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“…Studies show that posterior results are usually robust with respect to changes in these priors (see for example, Jafari Khaledi and Rivaz, 2009). But, the choice of the prior distribution for the range parameter demands more attention.…”

Section: Posterior Studymentioning

confidence: 98%

“…However, due to the model involves non-observed variables which their components are strongly dependent on each other, the conventional MCMC algorithms may converge slowly or even fail to converge. Besides, the Bayesian inferences largely depend on the choice of the prior distributions which could have an unpleasant influence on inferences (Jafari Khaledi and Rivaz, 2009). There are situations where there is little scientific theory or previous empirical evidence to suggest prior for a fully Bayesian model.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo approximation of likelihood function in spatial GLMMs through an empirical Bayes method

Rivaz

Khaledi

2016

Communications in Statistics - Simulation and Computation

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In spatial generalized linear mixed models (SGLMMs), statistical inference encounters problems, since random effects in the model imply high-dimensional integrals to calculate the marginal likelihood function. In this paper, we temporarily treat parameters as random variables and express the marginal likelihood function as a posterior expectation. Hence, the marginal likelihood function is approximated using the obtained samples from the posterior density of the latent variables and parameters given the data. However, in this setting, misspecification of prior distribution of correlation function parameter and problems associated with convergence of Markov chain Monte Carlo (MCMC) methods could have an unpleasant influence on the likelihood approximation. To avoid these challenges, we utilize an empirical Bayes approach to estimate prior hyperparameters. We also use a computationally efficient hybrid algorithm by combining inverse Bayes formula (IBF) and Gibbs sampler procedures. A simulation study is conducted to assess the performance of our method. Finally, we illustrate the method applying a data set of standard penetration test of soil in an area in south of Iran.

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Section: Posterior Studymentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Monte Carlo approximation of likelihood function in spatial GLMMs through an empirical Bayes method

Rivaz

Khaledi

2016

Communications in Statistics - Simulation and Computation

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“…However, the distribution of data were collected from a wide range of applications reveals asymmetry. Examples arise, for instance, in wind speed data (Zhu and Genton 2012), temperature data (North et al 2011), soil and air pollution data (Jafari Khaledi and Rivaz 2009;Zareifard and Jafari Khaledi 2013), precipitation data (Xu and Genton 2017) and diabetes data (Kristensen et al 2010). The skew-normal (SN) distribution, introduced by Azzalini (1985), has been used successfully to model data sets that have asymmetric behavior.…”

Section: Introductionmentioning

confidence: 99%

The polar-generalized normal distribution: properties, Bayesian estimation and applications

Faridi

Khaledi

2021

Stat Papers

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This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a separate scalar parameter. Explicit expressions for the cumulative distribution function, the density function and the moments were derived. The stochastic representation of the distribution facilitates implementing Bayesian estimation via the Markov chain Monte Carlo methods. Some real-life data as well as simulated data are analyzed to illustrate the flexibility of the distribution for modeling asymmetric bimodality.

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“…However, the distribution of data were collected from a wide range of applications reveals asymmetry. Examples arise, for instance, in wind speed data (Zhu and Genton, 2012), temperature data (North et al, 2011), soil and air pollution data (Jafari Khaledi and Rivaz, 2009; Zareifard and Jafari , precipitation data (Xu and Genton, 2017) and diabetes data (Kristensen et al, 2010). The skew-normal (SN) distribution, introduced by Azzalini (1985), has been used successfully to model data sets that have asymmetric behavior.…”

Section: Introductionmentioning

confidence: 99%

The polar-generalized normal distribution

Faridi¹,

Khaledi²

2020

Preprint

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Empirical Bayes spatial prediction using a Monte Carlo EM algorithm

Abstract: Spatial data, Prediction, Empirical Bayes, EM algorithm, Monte Carlo, Reference prior,

Cited by 9 publications

References 19 publications

Monte Carlo approximation of likelihood function in spatial GLMMs through an empirical Bayes method

Monte Carlo approximation of likelihood function in spatial GLMMs through an empirical Bayes method

The polar-generalized normal distribution: properties, Bayesian estimation and applications

The polar-generalized normal distribution

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