Test for independence between marks and points of marked point processes

Ecological data often involve measurements taken at irregularly spaced locations, e.g., the heights of trees in a forest. A useful approach to model such data is via a marked point process, where the marks (i.e., measurements) and points (i.e., locations) are often assumed to be independent. While a convenient assumption, this may not hold in practice. Schelather et al. (2003) proposed a simulation based approach to test this assumption. The purpose of this paper is to present a new method for testing the assumption of independence between the marks and points. Instead of considering a simulation approach, we derive analytical results that allow the test to be implemented via a conventional χ statistics. We illustrate the use of our approach by an application to a desert plant data example.