Inference for Thinned Point Processes, with Application to Cox Processes.

摘要

The topics of this reprint are statistical inference and state estimation for thinned point processes, especially Cox processes. Observation of a thinning of a point process represents a form of partial observation analogous in some senses to problems of missing data in the classical context of a random sample and in other senses to problems involving censored data. The thinning mechanism analyzed here is general enough to admit wide applicability in modeling, yet specific enough to permit precise results: points of an underlying point process N are deleted independently of one another but with probabilities depending on their locations. The resultant thinned point process N ( specifically, i.i.d. copies of N) is observable and from these observations it is desired to perform inference concerning the probability law of N and the thinning function p(x) (a point of N at x epsilon E is retained in N with probability p(x)).