IJPAM: Volume 53, No. 1 (2009)

ESTIMATING THE NUMBER OF OZONE PEAKS IN
MEXICO CITY USING A NON-HOMOGENEOUS POISSON
MODEL AND A METROPOLIS-HASTINGS ALGORITHM

Jorge A. Achcar$^1$, Gisela Ortiz-Rodríguez$^2$, Eliane R. Rodrigues$^3$
$^1$Faculdade de Medicina de Ribeirão Preto
Universidade de São Paulo - USP
Av. Bandeirantes, 3900
14049-900 - Ribeirão Preto - SP, BRAZIL
e-mail: achcar@fmrp.usp.br
$^{2,3}$Instituto de Matemáticas
Universidad Nacional Autónoma de México - UNAM
Area de la Investigación Científica
Circuito Exterior, Ciudad Universitaria
México, D.F., 04510, MÉXICO
$^2$e-mail: giselaortiz37@hotmail.com
$^3$e-mail: eliane@math.unam.mx


Abstract.In this paper we consider the problem of estimating the probability of having an air quality standard exceeded a certain number of times in a time interval of interest. A non-homogeneous Poisson model is used to study this problem. The rate function at which the Poisson events occur is given by $\lambda(t) > 0$, $t \geq 0$ which depends on some parameters to be estimated. These parameters are estimated using a Bayesian formulation based on a Metropolis-Hastings algorithm. A comparison of the performance of this algorithm with the performance of the WinBugs software is also given.

Received: March 7, 2009

AMS Subject Classification: 60J20, 60G55, 62F15, 62M99, 92F05

Key Words and Phrases: Metropolis-Hastings algorithm, Bayesian inference, non-homogeneous Poisson model

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 1