A non-homogeneous poisson model with spatial anisotropy applied to ozone data from Mexico City

Abstract

In this work we consider a non-homogenous Poisson model to study the behaviour of the number of times that a pollutant's concentration surpasses a given threshold of interest. Spatial dependence is imposed on the parameters of the Poisson intensity function in order to account for the possible correlation between measurements in different sites. An anisotropic model is used due to the nature of the region of interest. Estimation of the parameters of the model is performed using the Bayesian point of view via Markov chain Monte Carlo (MCMC) algorithms. We also consider prediction of the days in which exceedances of the threshold might occur at sites where measurements cannot be taken. This is obtained by spatial interpolation using the information provided by the sites where measurements are available. The prediction procedure allows for estimation of the behaviour of the mean function of the Handling Editor:

An application of a non-homogeneous Poisson model to study PM2.5 exceedances in Mexico City and Bogota

“…The value obtained was K sim = 144. Following [1] and as in [2], we have generated the exceedance days accordingly. Using these simulated days as observed exceedance days, we have applied the model with no change-points and run the MCMC algorithm to estimate α and σ using the Bayesian formulation.…”

State‐space prior distribution for parameter of nonhomogeneous Poisson spatiotemporal models

“…In other applications, in addition to studying the behavior of the occurrence rate of an event of interest over time, it may be essential to analyze the spatial behavior to identify areas of greater or lesser intensity and to find factors that influence the increase or decrease of such an event. In this sense, Rodrigues et al (2014) proposed a spatial model to study the behavior of ozone concentrations that exceeded the 0.11-ppm threshold in different locations in Mexico City between 2005 and 2009. This approximation assumes that the intensity function is of the Weibull type and introduces spatial dependence on both parameters, relaxing the assumption of isotropy in the specification of the spatial correlation structure.…”

Agricultural drought periods analysis by using nonhomogeneous poisson models and regionalization of appropriate model parameters

“…So, this limit (of SPI less than or equal to À1.0) was considered a threshold by Achcar et al (2016) to enumerate and analyze the drought periods using the NHPP model. NHPP models are commonly used to analyze the exceedances events like noise pollutions (Guarnaccia et al, 2015), the earthquake groundmotion intensities (Iervolino et al, 2014), and the air quality standards (Achcar et al, 2016;Achcar et al, 2008;Rodrigues et al, 2015). It provides us a way towards the point pattern of exceedance events (Cressie, 1992;Diggle, 2013).…”

“…For the NHPP models used for the count data analysis, the Bayesian approach is considered with various prior distributions to estimate the model parameters, commonly illustrated in previous literature (Guarnaccia et al, 2015;Leininger and Gelfand, 2017). The researcher commonly used the Bayesian approach for the estimation of parameters in various applications of different areas, i.e., in the analysis of air pollution data, in the software reliability analysis, in the drought analysis, and air quality standards (Bar-Lev et al, 1992;Kuo and Yang, 1996;Cid and Achcar, 1999;Achcar et al, 2008Achcar et al, , 2011Achcar et al, , 2016Rodrigues et al, 2015) .…”