Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes
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We propose a new fitting method to estimate the set of second-order parameters for the class of homogeneous spatio-temporal log-Gaussian Cox point processes. With simulations, we show that the proposed minimum contrast procedure, based on the spatio-temporal pair correlation function, provides reliable estimates and we compare the results with the current available methods. Moreover, the proposed method can be used in the case of both separable and non-separable parametric specifications of the correlation function of the underlying Gaussian Random Field. We describe earthquake sequences comparing several Cox model specifications.
KeywordsEarthquakes Log-Gaussian Cox processes Minimum contrast method Non-separable covariance function Spatio-temporal pair correlation function
We would like to thank the Associate Editor and the two anonymous Referees for their suggestions and comments, that considerably improved the manuscript. This paper has been supported by the national grant of the Italian Ministry of Education University and Research (MIUR) for the PRIN-2015 program (Progetti di ricerca di Rilevante Interesse Nazionale), “Prot. 20157PRZC4— Research Project Title Complex space-time modeling and functional analysis for probabilistic forecast of seismic events. PI: Giada Adelfio”. J. Mateu has been partially founded by Grants P1-1B2015-40 and MTM2016-78917-R.
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