Student’s-t process with spatial deformation for spatio-temporal data

Fidel Ernesto Castro Morales (), Dimitris N. Politis (), Jacek Leskow () and Marina Silva Paez ()
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Fidel Ernesto Castro Morales: UFRN
Dimitris N. Politis: University of California
Jacek Leskow: Cracow University of Technology
Marina Silva Paez: UFRJ

Statistical Methods & Applications, 2022, vol. 31, issue 5, No 2, 1099-1126

Abstract: Abstract Many models for environmental data that are observed in time and space have been proposed in the literature. The main objective of these models is usually to make predictions in time and to perform interpolations in space. Realistic predictions and interpolations are obtained when the process and its variability are well represented through a model that takes into consideration its peculiarities. In this paper, we propose a spatio-temporal model to handle observations that come from distributions with heavy tails and for which the assumption of isotropy is not realistic. As a natural choice for a heavy-tailed model, we take a Student’s-t distribution. The Student’s-t distribution, while being symmetric, provides greater flexibility in modeling data with kurtosis and shape different from the Gaussian distribution. We handle anisotropy through a spatial deformation method. Under this approach, the original geographic space of observations gets mapped into a new space where isotropy holds. Our main result is, therefore, an anisotropic model based on the heavy-tailed t distribution. Bayesian approach and the use of MCMC enable us to sample from the posterior distribution of the model parameters. In Sect. 2, we discuss the main properties of the proposed model. In Sect. 3, we present a simulation study, showing its superiority over the traditional isotropic Gaussian model. In Sect. 4, we show the motivation that has led us to propose the t distribution-based anisotropic model—the real dataset of evaporation coming from the Rio Grande do Sul state of Brazil.

Keywords: Student’s-t process; Spatio-temporal modeling; Spatial deformation; Markov Chain Monte Carlo; Heavy tails (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10260-022-00623-8

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