Potential mapping from geochemical surveys using a Cox process

Punctual occurrence phenomena are often modeled as Poisson point processes, sometimes with an inhomogeneous, unknown intensity, that is desired to be estimated from some covariables. Within this setting, we study the case in which the covariables form a regionalized geochemical composition of stream sediments, and the known punctual occurrences are existing mineral deposits, not collocated with the available explanatory data. This is modeled by assuming a two-layer stochastic process, where the observed Poisson log-intensity is taken as a balanced log-linear function of the geochemical composition of stream sediments, which coefficients must be estimated. Estimation is possible through a pseudolikelihood device based on generalized loglinear models, though the result intensity function appears to be valid only up to arbitrary scaling and addition of constants.