A nonhomogeneous Poisson process geostatistical model

This paper introduces a new geostatistical model for counting data under a space-time approach using nonhomogeneous Poisson processes, where the random intensity process has an additive formulation with two components: a Gaussian spatial component and a component accounting for the temporal effect....

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Bibliographic Details
Published in:Stochastic environmental research and risk assessment 2017-02, Vol.31 (2), p.493-507
Main Authors: Morales, Fidel Ernesto Castro, Vicini, Lorena, Hotta, Luiz K., Achcar, Jorge A.
Format: Article
Language:English
Subjects:
Air pollution
Algorithms
Aquatic Pollution
Bayesian analysis
Chemistry and Earth Sciences
Computational Intelligence
Computer Science
Computer simulation
Earth and Environmental Science
Earth Sciences
Effectiveness
Environment
Geostatistics
Markov analysis
Markov chains
Math. Appl. in Environmental Science
Mathematical models
Monte Carlo methods
Monte Carlo simulation
Normal distribution
Original Paper
Ozone
Physics
Poisson density functions
Poisson distribution
Pollution
Pollution levels
Probability Theory and Stochastic Processes
Statistics for Engineering
Waste Water Technology
Water Management
Water Pollution Control
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Summary:This paper introduces a new geostatistical model for counting data under a space-time approach using nonhomogeneous Poisson processes, where the random intensity process has an additive formulation with two components: a Gaussian spatial component and a component accounting for the temporal effect. Inferences of interest for the proposed model are obtained under the Bayesian paradigm. To illustrate the usefulness of the proposed model, we first develop a simulation study to test the efficacy of the Markov Chain Monte Carlo (MCMC) method to generate samples for the joint posterior distribution of the model’s parameters. This study shows that the convergence of the MCMC algorithm used to simulate samples for the joint posterior distribution of interest is easily obtained for different scenarios. As a second illustration, the proposed model is applied to a real data set related to ozone air pollution collected in 22 monitoring stations in Mexico City in the 2010 year. The proposed geostatistical model has good performance in the data analysis, in terms of fit to the data and in the identification of the regions with the highest pollution levels, that is, the southwest, the central and the northwest regions of Mexico City.
ISSN:1436-3240
1436-3259
DOI:10.1007/s00477-016-1275-x