next up previous
Next: Strauss Processes Up: Finite Point Processes Previous: Setup and Notation

Statistical Models

The opportunity to do statistics arises when we consider a statistical model specified by a family tex2html_wrap_inline2369 of unnormalized densities with respect to tex2html_wrap_inline2349 . The normalizing function of the family is

  equation310

Recall that the requirement that tex2html_wrap_inline3069 for all tex2html_wrap_inline2375 is implied by using the terminology `unnormalized density' for each of the tex2html_wrap_inline2495 .

Normalized densities of the family are defined by

  equation319

and the corresponding probability measures by

  equation324

Models of this type include Markov point processes (Ripley and Kelley, 1977) and nearest-neighbour Markov point processes (Baddeley and Møller, 1989). Another broad family is exponential family models in which tex2html_wrap_inline2495 has the form tex2html_wrap_inline3077 where t is a map from tex2html_wrap_inline2343 to tex2html_wrap_inline2943 and the parameter space tex2html_wrap_inline2427 is a subset of tex2html_wrap_inline2943 .



Charles Geyer
Fri Jul 5 15:26:21 CDT 1996