Spatial Sampling Design Based on Stochastic Complexity

A new methodology is introduced for spatial sampling design when the variable of interest cannot be directly observed, but information on it can be obtained by sampling a related variable, and estimation of the underlying model is required. An approach based on entropy has been proposed by Bueso, Angulo, and Alonso (1998, Environ. Ecol. Statist. 5, No. 1, 29–14) in the case where a model for the involved variables is given. However, in some cases a predetermined structure modelling the behaviour of the variables cannot be assumed. In this context, we derive criteria for solving the design problem based on the stochastic complexity theory and on the philosophy of the EM algorithm. For applying the proposed criteria a computational procedure is developed based on the supplemented EM algorithms. The methodology is illustrated with a numerical example.