Effective probability distribution approximation for the reconstruction of missing data

摘要

Spatially distributed 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 missing data. While environmental data often exhibit significant deviations from Gaussian behavior (rainfall, wind speed, and earthquakes being characteristic examples), only a few non-Gaussian joint probability density functions admit explicit expressions. In addition, random field models are computationally costly for big datasets. We propose an "effective distribution" approach which is based on the product of univariate conditional probability density functions modified by local interactions. The effective densities involve local parameters that are estimated by means of kernel regression. The prediction of missing data is based on the median value from an ensemble of simulated states generated from the effective distribution model. The latter can capture non-Gaussian dependence and is applicable to large spatial datasets, since it does not require the storage and inversion of large covariance matrices. We compare the predictive performance of the effective distribution approach with classical geostatistical methods using Gaussian and non-Gaussian synthetic data. We also apply the effective distribution approach to the reconstruction of gaps in large raster data.