We show how a spatial point process, where to each point there is associated a random quantitative mark, can be identified with a spatio-temporal point process specified by a conditional intensity function. For instance, the points can be tree locations, the marks can express the size of trees, and the conditional intensity function can describe the distribution of a tree (i.e., its location and size) conditionally on the larger trees. This enable us to construct parametric statistical models which are easily interpretable and where likelihood-based inference is tractable. In particular, we consider maximum likelihood based inference and tests for independence between the points and the marks.

Keywords: conditional intensity; likelihood ratio statistic; independence between points and marks; maximum likelihood; model checking; quantitative marks.