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November 2019 Spatiotemporal point processes: regression, model specifications and future directions
Dani Gamerman
Braz. J. Probab. Stat. 33(4): 686-705 (November 2019). DOI: 10.1214/19-BJPS444

Abstract

Point processes are one of the most commonly encountered observation processes in Spatial Statistics. Model-based inference for them depends on the likelihood function. In the most standard setting of Poisson processes, the likelihood depends on the intensity function, and can not be computed analytically. A number of approximating techniques have been proposed to handle this difficulty. In this paper, we review recent work on exact solutions that solve this problem without resorting to approximations. The presentation concentrates more heavily on discrete time but also considers continuous time. The solutions are based on model specifications that impose smoothness constraints on the intensity function. We also review approaches to include a regression component and different ways to accommodate it while accounting for additional heterogeneity. Applications are provided to illustrate the results. Finally, we discuss possible extensions to account for discontinuities and/or jumps in the intensity function.

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Dani Gamerman. "Spatiotemporal point processes: regression, model specifications and future directions." Braz. J. Probab. Stat. 33 (4) 686 - 705, November 2019. https://doi.org/10.1214/19-BJPS444

Information

Received: 1 February 2019; Accepted: 1 April 2019; Published: November 2019
First available in Project Euclid: 26 August 2019

zbMATH: 07120729
MathSciNet: MR3996312
Digital Object Identifier: 10.1214/19-BJPS444

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 4 • November 2019
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