J. Dvořák (2015)

Model fitting for space-time point patterns using projection processes

Proceedings of the 19th European Young Statisticians Meeting (ed. S. Nagy), Prague, Matfyzpress, 34-39.


Statistical inference for spatial and space-time point patterns recorded e.g. in ecological or epidemiological applications represents a challenging task. The data consists of a random collection of points {u1, ..., uN} observed in a compact observation window W, or, in the space-time setting, a random collection of space- time events {(u1,t1), ..., (uN,tN)} observed in W over a time period T. Both the number of observed points N and their locations are random. We focus our attention on the space-time clustered point patterns. We discuss the possibility to use dimension-reduction techniques to fit different parts of a space- time model separately. Specifically, we define the projections of the process to the spatial and temporal domain, respectively, and introduce a step-wise estimation procedure based on these projections. We also discuss the problem of possible cluster overlapping and the resulting loss of information in the projections and the challenges it presents for parameter estimation.


space-time point process, Cox process, minimum contrast estimation, K-function, projection process