Estimation of Poisson intensity using partially observed concomitant variables

In ecology, the spatial point pattern formed by the locations of organisms may be influenced by concomitant environmental variables (e.g., elevation, soil moisture, light intensity, etc.). The modulated Poisson process (a Poisson process whose log intensity is a linear function of concomitant spatial variables) is particularly well suited for modeling the effects of such variables. Maximum likelihood estimation of the parameters of a modulated Poisson process is straightforward when the values of the concomitant spatial variables are known at all locations in the region. This paper considers parameter estimation when the concomitant environmental variables are only observed for a sample of sites in the region. These methods are illustrated using data from a beech-magnolia forest in southern Georgia.