ABSTRACT
This chapter describes various classes of parametric point process models that are useful for scientific work. In any particular application, there will generally be an underlying physical mechanism that generates the point events that are observed, and which may be fully or partially understood. In building a model for these events, the modeler often seeks to represent or reflect that physical process, albeit in a highly simplified way. Thus, for example, if the point events are the locations of seedling trees, it will be natural to build a model that takes into account the positions of parent trees, the clustering of the seedlings around these, and perhaps also the prevailing wind direction, even if the exact process of seed generation and dispersal is not represented. Such a model is often termed “mechanistic,” and has interpretable parameters that relate to physical phenomena. In contrast, “descriptive” models aim to represent the statistical properties of the data and their dependence on explanatory variables without necessarily worrying about the physical mechanisms involved. For example, a model that involves inhibition between nearby events can be used to model the positions of ants’ nests (Harkness and Isham, 1983; see also Chapter 19, Section 19.4.2 of this volume for further discussion). The inhibition reflects competition for resources, but is not modeled directly.
