Spatial Statistics


Spatial statistics is a relatively new area of development and remains an area of active statistical research. Spatial data is distinguished by observations that are obtained at spatial locations in the plane or space. Time series processes attempt to model the correlations between responses at different time points. Similarly, with spatial data, the spatial correlation structure needs to be incorporated and modeled.

We are mainly interest in two problems. The first one deals with the correlation between two spatial sequences. Several coefficients have been defined to quantify the spatial association. One of them is the codispersion coefficient. Theoretical properties have been proved and applications in forest sciences and environmental sciences have been carried out. The second problem is related to the determination of effective sample size when the an available data set has spatial correlation. The main idea is quantify the sample size reduction due to spatial correlation. A new definition of effective sample size has been proposed. Currently, we are working to obtain asymptotic results for the estimated effective sample size and trying to characterize our notion of effective sample size when the coordinates of the data are uniformly distributed on a d-dimensional unit circle.

Members

  

Publications

  1. Porcu E, Allard D, Senoussi R. Anisotropy Models for spatial data. Mathematical Geosciences 2016;48(3):305-328. [Bibtex]
  2. Porcu E, Bevilacqua M, Hering A. S. On the flexibility of multivariate covariance models.. Statistical Science 2015;30(1):165-169. [Bibtex]
  3. Porcu E, Salazar E, Giraldo E. M. Spatial Prediction for Infinite-Dimensional Compositional Data.. Stochastic Env. Res. Risk Assessment 2015;29(7):1737-1749. [Bibtex]
  4. Porcu E, Daley D. J, Bevilacqua M. Classes of compactly supported covariance functions for multivariate random fields.. Stochastic Env. Res. Risk Assessment 2015;29(4):1249-1263. [Bibtex]
  5. Porcu E, Alonso-Malaver C, Giraldo E. M. Multivariate and Multiradial Schoenberg Measures with their Dimension Walk. J. of Multivariate Analysis 2015;133:251-265. [Bibtex]
  

Projects

  1. FONDECYT 1140580: Influence diagnostics and residual analysis in inference functions with applications to longitudinal data
  2. Fondecyt 1120048. Association Characteristics Between Two Spatial Processes and Reduction of Sample sizes in Spatial Statistics.
  3. Proyecto de Inserción CONICYT. Fortalecimiento del Área Estadística en el Departamento de Matemática de la USM
  4. Proyecto CCTVal FB/01RV/11. Estimación no Paramétrica del Coeficiente de Codispersión: Aspectos Teóricos y Prácticos
  5. PROSUL 490429/2008-4, CNPq-Brazil: Desenvolvimento de métodos de diagnóstico e teoria assintótica em modelos de regressão

JA slide show