A latent class MDS model with spatial constraints for non-stationary spatial covariance estimation

Abstract

Multidimensional scaling (MDS) has played an important role in non-stationary spatial covariance structure estimation and in analyzing the spatiotemporal processes underlying environmental studies. A combined cluster-MDS model, including geographical spatial constraints, has been previously proposed by the authors to address the estimation problem in oversampled domains in a least squares framework. In this paper is formulated a general latent class model with spatial constraints that, in a maximum likelihood framework, allows to partition the sample stations into classes and simultaneously to represent the cluster centers in a low-dimensional space, while the stations and clusters retain their spatial relationships. A model selection strategy is proposed to determine the number of latent classes and the dimensionality of the problem. Real and artificial data sets are analyzed to test the performance of the model.

Second-order non-stationary modeling approaches for univariate geostatistical data

“…A transformation to higher dimensions may be appropriate at the expense of the visualization and the interpretation of the deformed space. Vera et al (2008Vera et al ( , 2009 propose an approach which involves partitioning the data into classes and representing the centers of classes in a low dimensional space while the data locations and classes maintain their spatial relationships. This method is applied to wind speed data.…”

Complex bimatrix variate generalised beta distributions

“…Given the genesis of bimatrix variate generalised beta distributions, such distributions may allow us, in some sense, to model the learning problem. Statistical approaches to MDS have been studied assuming independence between times (without learning) in the univariate case by Ramsay (1982) and by Vera et al (2008).…”

Estimation of space deformation model for non-stationary random functions

“…Perrin and Meiring [13], Perrin and Senoussi [14], Perrin and Meiring [15], Genton and Perrin [16], Porcu et al [17] established some theoretical properties about uniqueness and richness of this class of non-stationary models. Some adaptations have been proposed recently by Castro Morales et al [18], Bornn et al [19], Schmidt et al [20], Vera et al [21,22].…”