Seminario Dottorato: Finite and countable mixtures

Wednesday 24 March 2010 - Cecilia Prosdocimi

ARGOMENTI: Seminari Dottorato

Wednesday 24 March 2010 h. 15:00, room 2AB/45
Cecilia Prosdocimi (Universita` di Padova - Dip. Mat.)
"Finite and countable mixtures"

The present talk deals with finite and countable mixtures of independent identically distributed (i.i.d.) sequences and of Markov chains. After an easy introduction on mixture models and their main properties, we focus on binary exchangeable sequences. These are mixtures of i.i.d. sequences by de Finetti theorem. We present a necessary and sufficient condition for an exchangeable binary sequence to be a mixture of a finite number of i.i.d. sequences. If this is the case, we provide an algorithm which completely solves the stochastic realization problem. In the second part of the talk we focus on partially exchangeable sequences, that are known to be mixtures of Markov chains after the work of Diaconis and Freedman, and Fortini et al. later. We present a characterization theorem for partially exchangeable sequences that are mixtures just of a finite or countable number of Markov chains, finding a connection with Hidden Markov Models. Our result extends an old theorem by Dharmadhikari on finite and countable mixtures of i.i.d. sequences.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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