Learning Markov Processes with Latent Variables From Longitudinal Data

Résumé

We present a constructive proof of (nonparametric) identication of the parameters of a bivariate Markov chain when only one of the two random variables is observable. This setup generalizes the hidden Markov model in various useful directions, allowing for state dependence in the observables and allowing the transition kernel of the hidden Markov chain to depend on past observables. We give conditions under which the transition kernel and the distribution of the initial condition are both identied (up to a permutation of the latent states) from the joint distribution of four (or more) time-series observations.

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Référence

Ayden Higgins et Koen Jochmans, « Learning Markov Processes with Latent Variables From Longitudinal Data », TSE Working Paper, n° 22-1366, septembre 2022, révision mai 2024.