Venezuelan Rainfall Data Analysed by Using a Bayesian Space-time Model

• Published in: Applied statistics 1999, Vol.48 (3), p.345-362
• Main Authors: Sansó, Bruno, Guenni, Lelys
• Format: Article
• Language: English
• Subjects: Bayesian estimation; Correlations; Covariance matrices; Data models; Exact sciences and technology; Gaussian distributions; Inference from stochastic processes; time series analysis; Markov chain Monte Carlo method; Markov chains; Mathematics; Modeling; Multivariate analysis; Parametric models; Probability and statistics; Rain; Rainfall modelling; Sciences and techniques of general use; Space-time models; Spacetime; Spatial models; Statistics; Truncated normal model
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/1467-9876.00157

We consider a set of data from 80 stations in the Venezuelan state of Guarico consisting of accumulated monthly rainfall in a time span of 16 years. The problem of modelling rainfall accumulated over fixed periods of time and recorded at meteorological stations at different sites is studied by using a model based on the assumption that the data follow a truncated and transformed multivariate normal distribution. The spatial correlation is modelled by using an exponentially decreasing correlation function and an interpolating surface for the means. Missing data and dry periods are handled within a Markov chain Monte Carlo framework using latent variables. We estimate the amount of rainfall as well as the probability of a dry period by using the predictive density of the data. We considered a model based on a full second-degree polynomial over the spatial co-ordinates as well as the first two Fourier harmonics to describe the variability during the year. Predictive inferences on the data show very realistic results, capturing the typical rainfall variability in time and space for that region. Important extensions of the model are also discussed.