Student’s-t process with spatial deformation for spatio-temporal data
Authors:
- Fidel Ernesto Castro Morales,
- Dimitris N. Politis,
- Jacek Leskow,
- Marina Silva Paez
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.
- Record ID
- CUTa498e39333f34072a12df8559e294967
- Publication categories
- ;
- Author
- Journal series
- Statistical Methods and Applications, ISSN 1618-2510, e-ISSN 1613-981X
- Issue year
- 2022
- Vol
- 31
- No
- 5
- Pages
- 1099-1126
- Other elements of collation
- mapy; tab.; wykr.; Bibliografia (na s.) - 1124-1125; Oznaczenie streszczenia - Abstr.; Data udostępnienia on-line - 2022-03-01; Numeracja w czasopiśmie - Vol. 31, Iss. 5
- Keywords in English
- student’s-t process, spatio-temporal modeling, spatial deformation, Markov Chain Monte Carlo, heavy tails
- ASJC Classification
- ;
- DOI
- DOI:10.1007/s10260-022-00623-8 Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s10260-022-00623-8 Opening in a new tab
- Language
- eng (en) English
- Score (nominal)
- 70
- Score source
- journalList
- Score
- Publication indicators
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTa498e39333f34072a12df8559e294967/
- URN
urn:pkr-prod:CUTa498e39333f34072a12df8559e294967
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.