Time series: from Markov models to hidden Markov models
Simona Maria Cocco, Rémi Monasson, Francesco Zamponi · 2022
Abstract So far, we have considered inference problems in which time played no role. In many applications, however, data are time series produced by a dynamical process. How can we infer the underlying rules defining this process? We will address this question in two frameworks: a simple one, in which measurements give direct access to the dynamical sequence of the states visited by the system, and a more complex one, in which data provide indirect knowledge about the states. In the latter situation, we will study a powerful approach, called hidden Markov models, and will see how to efficiently answer several questions of interest, of increasing difficulty: how to compute the likelihood of a time series of observations? How to infer the corresponding ‘hidden’ states? How to infer the model parameters?