IJPAM: Volume 48, No. 3 (2008)

A TRANS-DIMENSIONAL MCMC ALGORITHM
TO ESTIMATE THE ORDER OF A MARKOV CHAIN:
AN APPLICATION TO OZONE PEAKS IN MEXICO CITY

Luis J. Álvarez$^1$, Eliane R. Rodrigues$^2$
$^1$Instituto de Matemáticas - UNAM - Unidad Cuernavaca
Av. Universidad, S/N - Lomas de Chamilpa
Morelos, Cuernavaca, 62210, MEXICO
e-mail: lja@matcuer.unam.mx
$^2$Instituto de Matemáticas - UNAM
Area de la Investigación Científica
Circuito Exterior, Ciudad Universitaria
México, D.F., 04510, MEXICO
e-mail: eliane@math.unam.mx


Abstract.In this paper the problem of estimating the order $K \geq 0$ of a Markov chain is addressed. In order to do so, we assume that ozone peaks follow a time-homogeneous Markov chain of order $K$. This order is estimated using a trans-dimensional Markov chain Monte Carlo (MCMC) algorithm. Once $K$ is estimated it is possible to obtain estimates for the transition matrix of the chain. Results are applied to ozone data provided by the Mexico City monitoring network. Prediction about the probability of having an ozone peak in a given time into the future given some present and/or past conditions may be obtained using the estimated transition matrix of the chain.

Received: May 26, 2008

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

Key Words and Phrases: trans-dimensional MCMC, Bayesian inference, inference in stochastic processes, ozone peaks

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 3