Title: Effective probability distributions for spatially dependent processes
Authors: Dionissios Hristopulos - Technical University of Crete (Greece)
Anastassia Baxevani - University of Cyprus (Cyprus) [presenting]
Abstract: Spatially distributed physical processes can be modeled as random fields. The complex spatial dependence is then incorporated in the joint probability density function. Knowledge of the joint probability density allows predicting the field values at points where measurements are missing. The probability distribution of spatially dependent processes often exhibits significant deviations from Gaussian behavior. However, only a few non-Gaussian joint probability density models admit explicit expressions. In addition, spatial random field models based on Gaussian or non-Gaussian joint densities incur formidable computational costs for big datasets. We propose an ``effective distribution'' approach which replaces the joint probability density with a product of univariate conditional probability density functions modified by a local interaction term. The effective densities involve localized parameters that link the densities at different locations. The prediction of the field at unmeasured locations is formulated in terms of the respective effective distribution and local constraints. We also propose a sequential simulation approach for generating multiple field realizations based on the effective distribution approach. The effective probability density model can capture non-Gaussian dependence, and it can be applied to large spatial datasets, since it does not require the storage and inversion of large covariance matrices.