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Statistical Inference for Point Process Models of Rainfall
Author(s) -
Smith James A.,
Karr Alan F.
Publication year - 1985
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr021i001p00073
Subject(s) - point process , cox process , inference , mathematics , selection (genetic algorithm) , statistical inference , class (philosophy) , model selection , estimation theory , stochastic process , stochastic modelling , set (abstract data type) , renewal theory , computer science , statistics , artificial intelligence , poisson distribution , poisson process , programming language
In this paper we develop maximum likelihood procedures for parameter estimation and model selection that apply to a large class of point process models that have been used to model rainfall occurrences, including Cox processes, Neyman‐Scott processes, and renewal processes. The statistical inference procedures are based on the stochastic intensity λ( t ) = lim s→0, s >0 (1/ s)E[N ( t + s ) − N(t )| N(u ), u < t ]. The likelihood function of a point process is shown to have a simple expression in terms of the stochastic intensity. The main result of this paper is a recursive procedure for computing stochastic intensities; the procedure is applicable to a broad class of point process models, including renewal Cox process with Markovian intensity processes and an important class of Neyman‐Scott processes. The model selection procedure we propose, which is based on likelihood ratios, allows direct comparison of two classes of point processes to determine which provides a better model for a given data set. The estimation and model selection procedures are applied to two data sets of simulated Cox process arrivals and a data set of daily rainfall occurrences in the Potomac River basin.