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Cox Point Processes: Why One Realisation Is Not Enough
Author(s) -
Micheas Athanasios C.
Publication year - 2019
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12308
Subject(s) - point process , cox process , realisation , poisson point process , point (geometry) , poisson distribution , process (computing) , class (philosophy) , computer science , function (biology) , mathematics , poisson process , statistical physics , statistics , econometrics , artificial intelligence , physics , geometry , quantum mechanics , evolutionary biology , biology , operating system
Summary We review a rich class of point process models, Cox point processes, and illustrate the necessity of more than one observation (point patterns) in performing parameter estimation. Furthermore, we introduce a new Cox point process model by treating the intensity function of the underlying Poisson point process as a random mixture of normal components. The behaviour and performance of the new model are compared with those of popular Cox point process models. The new model is exemplified with an application that involves a single point pattern corresponding to earthquake events in California, USA.