Brazilian Journal of Probability and Statistics

Spatiotemporal point processes: regression, model specifications and future directions

Dani Gamerman

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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.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 4 (2019), 686-705.

Dates
Received: February 2019
Accepted: April 2019
First available in Project Euclid: 26 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1566806428

Digital Object Identifier
doi:10.1214/19-BJPS444

Mathematical Reviews number (MathSciNet)
MR3996312

Zentralblatt MATH identifier
07120729

Keywords
Data augmentation discretization dynamic Gaussian processes partition models spatial interpolation

Citation

Gamerman, Dani. Spatiotemporal point processes: regression, model specifications and future directions. Braz. J. Probab. Stat. 33 (2019), no. 4, 686--705. doi:10.1214/19-BJPS444. https://projecteuclid.org/euclid.bjps/1566806428


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