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Fwd: Seminario IMQ, 15 dicembre 2005 h. 16.30
Seminario 15 dicembre 2005 h. 16.30
Aula IMQ, stanza n. 137
Antonio Lijoi
Universita' di Pavia
TITOLO: Clustering in Bayesian hierarchical mixture models
ABSTRACT
It is common practice to exploit random discrete probability measures as
a basic building block in hierarchical mixture models. In this framework
the number of distinct observations (within a sample of size n)
generated by such a prior takes on the interpretation of prior
distribution on the number of components.
Here we concentrate on a random probability measure giving rise to a
Gibbs partition of type sigma (see Gnedin and Pitman, 2004), where sigma
is some parameter in [0,1). This includes as special cases the Dirichlet
process, the stable process and the normalized inverse-Gaussian process.
We provide expressions for the prior and posterior distribution of the
number of distinct observations and describe the asymptotic behavious of
the number of clusters as the sample size increases. By resorting to a
few illustrations we point out a reinforcement mechanism acting when
sigma does not equal 0.
Pietro Muliere
Istituto Metodi Quantitativi
Università L. Bocconi
Viale Isonzo, 25
20135 Milano - Italy
Tel. 0039 02 58365623
Fax 0039 02 58365630
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