06/D111
Inferencia y simulación en procesos estocásticos espaciales IV
Inference and simulation in stochastic spatial processes IV
Director: DIBLASI, Ángela Magdalena
Correo electrónico: angelad@uncu.edu.ar
Integrantes: NARDECCHIA, Graciela Lucía; JULIÁN, Francisca; NARVAEZ, Ana María; ZABAL, María Elena; DÁMELIO, Adriana; REPETTO, Liliana; REY TUDELA, Elsa; MORENO, Amable; CAVALLER, Daniel; MAGLIONE, Dora
Summary: In the previous research Project, Inference and simulation in Spatial Stochastic Processes, the analysis of non stationary spatial processes modelled through an addition of two terms was carried out. In this approach, one of the terms is assumed to gather the large scale variation or trend and another one is the representative of a small scale variation or covariance structure. This model can be fitted by its transformation in a stationary process by means of elimination of the trend. Some applications for modelling the behaviour of rains in the Patagonia and the temperature in Argentina were performed. However, this model is not realistic for some problems in practice as data dealt with the cost of property in the surrounding area of Mendoza city. In the previous project these data were modelling resorting to a trend with local variability through smoothing techniques as splines and loess. These smoothers allow to capture the mean spatial variability in a neighbourhood. In the analyzed data, a nugget effect variogram was a result of polishing the trend with these smoothers. In other situations, these models are not adequate when the term related to the covariance structure cannot be assumed stationary globally but in a neighbourhood of some fixed points in the space. In this context, the spatial structure is not stationary but it can be considered as an extension of a stationary one. Yet, the estimation of the parameters of these models is still and opened problem. The likelihood estimation of the parameters leads to highly biased estimators. Under additional assumptions, Bayesian estimators through MCMC methodology were calculated. These estimators are efficient but the computational cost may result unmanageable. In this project, a nonparametric methodology for a local stationary structure will be considered. Spatial exploratory techniques will be focused to find different patterns of spatial covariance. Spatial methodologies to cope with models for pricing will be also analyzed. In this context, spatial dependency for AIDS (Almost Ideal Demand Systems) models will be incorporated for data where the assumption of spatial independency is not realistic. Applications of different statistical methodologies to environmental and economic data are also one of the aids of this project. Finally, a deep analysis of different statistical problems will result in an increasing the background.