Bayesian Modelling of Rainfall Data by Using Non-Homogeneous Hidden Markov Models and Latent Gaussian Variables

Abstract

Summary We present a non-homogeneous hidden Markov model for the spatiotemporal analysis of rainfall data, within a subjective Bayesian framework. In this model, daily rainfall patterns are driven by a small number of unobserved states, interpreted as states of the weather, that evolve in time according to a first-order non-homogeneous Markov chain, with transition probabilities dependent on time varying atmospheric data. The weather states alone do not account for all the space–time structure in the data and so we introduce latent multivariate normal random variables in a flexible model for the probability of rain and the distribution of non-zero rainfall amounts. In the resulting hierarchical non-homogeneous hidden Markov model, rainfall occurrences and non-zero rainfall amounts are spatially dependent and conditionally Markov in time, given the weather state. We build a prior distribution that conveys genuine initial beliefs and apply the model and inferential procedures to data from a network of 12 sites located throughout the UK.