To assume that observations follow a normal distribution (or symmetric) is a common assumption in models with spatial structure. However, this assumption can be unrealistic, hidding important characteristics of the underlying variation present in the data. Kim and Mallick (2004) and Hosseini, Eidsvik and Mohammadzadeh (2011) show through simulation that a misspecification of the distribution of spatial process can bias the estimation of the parameters, so make harder spatial prediction. Therefore, it is convinient to consider parametric families of ditributions that are flexible and capable of capturing a variety of symmetric as well as asymmetric behaviors, in which it includes the symmetric distributios (normal, Student-t, slash, contaminated normal) as special cases and it produces robust estimation in the considered model. In this way, the class of distributions of scale of mixtures of skew-normal (SMSN) (Branco and Dey, 2001; Lachos, Ghosh and Arellano-Valle, 2010) is interesting because it includes the symmetric and asymmetric versions of the distributions Student-t, slash, contaminated normal, power exponential, Pearson VII, and others, with all of them with heavier tail than the normal distribution, producing a robust estimation (and inference) at the considered model.The objective of this project is to present an inferential Baeysian study in spatial data models using more robust distributions than the skew-normal distribution, that is, using the class of scale of mixture of skew-normal distributions. The new model will be refered as SMSN-SP. Moreover, diagnostics studies will be presented based on the divergence measure of Kullback--Leibler, like discussed in Lachos, Bandyopadhyay and Dey (2011). In the estimation process, a Gibbs sampler will be used with implemenation in R, C++ and WinBUGS.The purpose of this project is to contribute positively to the development in the statistical research field, creating new results in models with pratical interest, extending and complementing some of the skew-normal results found, for example, in Kim and Mallick (2004); Hosseini, Eidsvik and Mohammadzadeh (2011); Karimi and Mohammadzadeh (2010); Zhang and Abdel El-Shaarawi (2010); Nathoo and Ghosh (2010); Prates et. al. (2010a); and others.
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