Department of Statistical Science
Duke University
presents:
Vincent Granville
granvill@niss.rti.org
NISS
RTP, NC
"Stochastic Models for Hourly Rainfall Time Series: Fitting and Statistical Analysis Based on Markov Chain Monte Carlo Methods"
Abstract: We propose a MCMC methodology to estimate all the components of the Bartlett-Lewis process of cells and storms studied by Rodriguez-Iturbe in hydrology. We focus on non Gaussian time series of hourly rainfall aggregates, for which we want to recover the underlying stochastic time-continuous rainfall intensity function. The investigated parametric model is associated with a likelihood function, and we use the Gibbs sampler to draw posterior deviates of the parameters in a Bayesian framework, conditionally on the data. The Gibbs sampler incorporates a Metropolis-Hastings step to sample the internal features (cell durations, cell lengths, etc.) of the model. The methodology is associated with reversible jumps and also incorporates birth and death steps. Non informative priors are used. We perform the simulations on a real data set of hourly rainfall measurements, and we exhibit a lack of fit with the theoretical model. To improve some of the inefficiencies of the model, we generalize it, considering a joint bivariate negatively correlated exponential distribution for the cell durations and cell lengths. The MCMC methodology is then extended to handle this new model. Model fitting is still further improved by applying post-processing rescaling and smoothing-sharpening techniques on the unconditional simulated rainfall amounts. Some of the issues considered here are missing data, assessing the convergence of the algorithm, asymptotic relationships and prediction.
January 31, 1997
4:00 pm - 5:00 pm
116 Old Chem Building Any questions concerning the seminar may be addressed to Cheryl McGhee @ [919] 684-8029 or e-mail cheryl@stat.duke.edu. Please contact the author(s) directly for reprints etc.