Analysis of Ozone Behaviour in the City of Puebla-Mexico Using Non-Homogeneous Poisson Models with Multiple Change-Points

Abstract

In this work, some non-homogeneous Poisson models are considered to study the behaviour of ozone in the city of Puebla, Mexico. Several functions are used as the rate function for the non-homogeneous Poisson process. In addition to their dependence on time, these rate functions also depend on some parameters that need to be estimated. In order to estimate them, a Bayesian approach will be taken. The expressions for the distributions of the parameters involved in the models are very complex. Therefore, Markov chain Monte Carlo algorithms are used to estimate them. The methodology is applied to the ozone data from the city of Puebla, Mexico.

A change-point detection and clustering method in the recurrent-event context

“…Starting from K initial centroids, we assign each object to the centroid with the largest similarity, and then update the centroids using Eqs. ( 4)- (5). We repeat the process until the partition does not change.…”

“…The NHPP is a Poisson process whose intensity function is not a constant over time [24, p. 32]. Examples include detecting the change-points in the ozone level by a Bayesian method [5], and proposing non-parametric estimators for the change-point when there were multiple subjects [10].…”

A non-parametric Bayesian change-point method for recurrent events

“…Recurrent events arise in many applications such as medical, engineering, and transportation research when a subject or sampling unit experiences one or more types of event multiple times longitudinally. For example, recurrent-event models can be applied to the accident or safety critical event history of drivers in Naturalistic Driving Studies (NDS) [27,30], the repair history of manufactured items or processes [45], episodes of recurrent disease in patients [12], and the recurrence of natural phenomena [7]. The intensity of the recurrent events is in general not constant and could change over time.…”

“…The majority of existing literature on recurrent-event change-point detection assumes a non-homogeneous Poisson process (NHPP) with an intensity function changing over time [44, p. 32]. Cruz-Juárez et al [7] analyzed the behavior of ozone in a Mexican city using an NHPP with multiple change-points under a Bayesian framework. Frobish et al [13] proposed two semi-parametric estimators of change-points in an NHPP setup for multiple individuals.…”

Analyzing the risk of mass shootings in the United States

“…A Bayesian approach is an unsupervised method that detects when the change point occurs based on a probabilistic approach (Raftery and Akman, 1986). The Bayesian change-point methods have been applied to various change points detection problems, such as ozone measurements in Mexico City (Achcar et al, 2010;Cruz-Juárez et al, 2016) and the risk analysis of teenage drivers (Li, 2015;Li et al, 2018Li et al, , 2017Li et al, , 2020a.…”