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Estimation of the intensity function of an inhomogeneous Poisson process with a change‐point
Author(s) -
Ng Tin Lok J.,
Murphy Thomas B.
Publication year - 2019
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11514
Subject(s) - markov chain monte carlo , point process , intensity (physics) , piecewise , function (biology) , poisson distribution , mathematics , parametric statistics , statistics , cox process , bayesian probability , mathematical optimization , poisson process , mathematical analysis , physics , quantum mechanics , evolutionary biology , biology
Recent work on point processes includes studying posterior convergence rates of estimating a continuous intensity function. In this article, convergence rates for estimating the intensity function and change‐point are derived for the more general case of a piecewise continuous intensity function. We study the problem of estimating the intensity function of an inhomogeneous Poisson process with a change‐point using non‐parametric Bayesian methods. An Markov Chain Monte Carlo (MCMC) algorithm is proposed to obtain estimates of the intensity function and the change‐point which is illustrated using simulation studies and applications. The Canadian Journal of Statistics 47: 604–618; 2019 © 2019 Statistical Society of Canada