Bayesian modelling of rainfall data by using non-homogeneous hidden Markov models and latent Gaussian variables

Abstract

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.