Geostatistical Interpolation of Rate Data Using Poisson Kriging

Historical Background

Kriging is a generalized least-square regression algorithm to predict spatial attributes at unsampled times and locations (Journel and Huijbregts, 1978). This geostatistical technique was originally developed to analyze continuous and categorical mining data. As the field of application of geostatistics expanded, there was a need to adapt these tools to the treatment of spatial count data which are routinely collected in many disciplines, such as ecology (e.g., bird counts), agronomy (e.g., weed counts), epidemiology (e.g., disease counts), or criminology (e.g., homicide counts). Count data are often transformed into rates through division by a quantity that represents observation or sampling efforts. For example, bird counts can be divided by the number of field trips or duration of observation to derive a measure of population abundance. Similarly, the number of weeds can be divided by the area of observation to calculate spatial density. Division of disease...