Bayesian methods for time series with mixed and mixture distributions with an application to daily rainfall data

Abstract

A mixture model can be used to represent two or more sub-populations. A special case is when one of the sub-populations has a degenerate (or discrete) distribution, and another has a continuous distribution. This leads to a mixed distribution. For example, daily rainfall data contain zero and positive values. This can be represented using two processes: an amount process and an occurrence process. This thesis is concerned with Bayesian time series models for non-independent mixturedistributed data, especially in the case of mixed distributions. Particular attention is given to the relationship between the occurrence and amount processes. The main application in the thesis is to daily rainfall data from weather stations in Italy and the United Kingdom. Firstly, the models for univariate rainfall series are developed. These are then extended to multivariate models by developing spatiotemporal models for rainfall at several sites, giving attention to how the spatiotemporal dependencies affect both the occurrence and amount processes. For the case of the British data, the models involve dependence on the Lamb weather types. Seasonal effects are included for all models. Posterior distributions of model parameters are computed using Markov chain Monte Carlo (MCMC) methods.