Application of hidden Markov and related models to earthquake studies

Abstract

Discrete valued hidden Markov Models (HMMs) are used to model time series of event counts in several scientific fields like genetics, engineering, seismology and finance. In its general form the model consists of two parts: the observation sequence and an unobserved sequence of hidden states that underlies the data and consist a Markov chain. Each state is characterized by a specific distribution and the progress of the hidden process from state to state is controlled by a transition probability matrix. We extend the theory of HMMs to the multivariate case and apply them to seismological data fromdifferent seismotectonic environments. This extension is not straightforward and it is achieved gradually by assuming different multivariate distributions to describe each state of the model.