APPROXIMATE BAYESIAN ANALYSIS OF SPATIO-TEMPORAL DATA USING A GAUSSIAN MARKOV RANDOM FIELD

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HOSSEINI FATEMEH; HOMAYONFAL ELHAM

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Journal: JOURNAL OF STATISTICAL SCIENCES Year:2017 | Volume:10 | Issue:2 Page(s): 233-260

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Title

APPROXIMATE BAYESIAN ANALYSIS OF SPATIO-TEMPORAL DATA USING A GAUSSIAN MARKOV RANDOM FIELD

Author(s)

HOSSEINI FATEMEH | HOMAYONFAL ELHAM | Issue Writer Certificate

Keywords

SPATIO-TEMPORAL DATAQ2

GAUSSIAN MARKOV RANDOM FIELDQ2

INTEGRATED NESTED LAPLACE APPROXIMATIONQ2

STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONSQ2

Abstract

Hierarchical spatio-temporal models are used for modeling space-time responses and temporally and spatially correlations of the data is considered via Gaussian latent random field with Matérn covariance function. The most important interest in these models is estimation of the model parameters and the latent variables, and is predict of the response variables at new locations and times. In this paper, to analyze these models, the Bayesian approach is presented. Because of the complexity of the posterior distributions and the full conditional distributions of these models and the use of Monte Carlo samples in a Bayesian analysis, the computation time is too long. For solving this problem, Gaussian latent random field with Matern covariance function are represented as a GAUSSIAN MARKOV RANDOM FIELD (GMRF) through the STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS (SPDE) approach. Approximatin Baysian method and INTEGRATED NESTED LAPLACE APPROXIMATION (INLA) are used to obtain an approximation of the posterior distributions and to inference about the model. Finally, the presented methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 2013.

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APA: Copy

HOSSEINI, FATEMEH, & HOMAYONFAL, ELHAM. (2017). APPROXIMATE BAYESIAN ANALYSIS OF SPATIO-TEMPORAL DATA USING A GAUSSIAN MARKOV RANDOM FIELD. JOURNAL OF STATISTICAL SCIENCES, 10(2 ), 233-260. SID. https://sid.ir/paper/124149/en

Vancouver: Copy

HOSSEINI FATEMEH, HOMAYONFAL ELHAM. APPROXIMATE BAYESIAN ANALYSIS OF SPATIO-TEMPORAL DATA USING A GAUSSIAN MARKOV RANDOM FIELD. JOURNAL OF STATISTICAL SCIENCES[Internet]. 2017;10(2 ):233-260. Available from: https://sid.ir/paper/124149/en

IEEE: Copy

FATEMEH HOSSEINI, and ELHAM HOMAYONFAL, “APPROXIMATE BAYESIAN ANALYSIS OF SPATIO-TEMPORAL DATA USING A GAUSSIAN MARKOV RANDOM FIELD,” JOURNAL OF STATISTICAL SCIENCES, vol. 10, no. 2 , pp. 233–260, 2017, [Online]. Available: https://sid.ir/paper/124149/en

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