Maximum likelihood estimation of the dynamic coregionalization model with heterotopic data

The information content of multivariable spatio-temporal data depends on the underlying spatial sampling scheme. The most informative case is represented by the isotopic configuration where all variables are measured at all sites. The opposite case is the completely heterotopic case where different variables are observed only at different locations. A well known approach to multivariate spatio-temporal modelling is based on the linear coregionalization model (LCM).In this paper, the maximum likelihood estimation of the heterotopic spatio-temporal model with spatial LCM components and temporal dynamics is developed. In particular, the computation of the estimates is based on the EM algorithm and two solutions are proposed: one is based on the more cumbersome exact maximization of the a posteriori expected log likelihood and the other is an approximate closed-form solution. Their properties are assessed in terms of bias and efficiency through an example of air quality dinamic mapping using satellite data and a Monte Carlo simulation campaign based on a large data set.