IJPAM: Volume 62, No. 1 (2010)

A BAYESIAN ESTIMATION OF THE PROBABILITY OF
ERUPTION PATTERNS OF THE MEXICAN VOLCANO
VOLCÁN DE COLIMA

Luis Javier Álvarez$^1$, Eliane R. Rodrigues$^2$
$^1$Instituto de Matemáticas - Unidad Cuernavaca
Universidad Nacional Autónoma de México - UNAM
México, D.F., 04510, MEXICO
e-mail: lja@matcuer.unam.mx
$^2$Instituto de Matemáticas
Universidad Nacional Autónoma de México - UNAM
Area de la Investigación Científica
Circuito Exterior, Ciudad Universitaria
México, D.F., 04510, MEXICO
e-mails: eliane@math.unam.mx


Abstract.In this paper we use a Markov chain model and real data of volcanic activity from Volcán de Colima-Mexico to estimate the probability of having a volcanic activity of interest with a given intensity. The data used here correspond to the activity pattern during the years 1893-1905. We assume that successive activities presented by the volcano follow a Markov chain of order $K$. This order is considered a random variable assuming values on a suitable set. Using a Bayesian approach we estimate the most likely order of the chain and the respective transition matrix. Based on these results the probability of having an activity with an intensity of interest is estimated.

Received: December 21, 2009

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

Key Words and Phrases: Bayesian inference, Markov chain models, volcanic activity

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 1