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Annuncio seminario
Seminari del Dipartimento di Scienze Statistiche, Universita' di Perugia,
Aula Interna del Dipartimento.
Prof. Guido Consonni -- Universita' di Pavia
Data: Venerdi' 30 aprile 2004 ore 15.00
Titolo : Priors for conditionally reducible multivariate exponential
families
Abstract:
If the joint density of a multivariate natural exponential family
can be written as a product of conditional densities, each being
an exponential family with respect to a suitable transition
kernel, then the family is said to be conditionally reducible.
Relationships between conditional reducibility and the the
existence of cuts are established. Conditionally reducible
families may be labelled in terms of variation- and
likelihood-independent parameters. From a Bayesian viewpoint,
this allows to generate
families of enriched conjugate priors which generalize the
standard conjugate ones, while retaining the usual simplicity of
closed-form prior-to-posterior analysis. The above
parameterization is also expedient to obtain reference priors (and
Jeffreys priors as a special case).
The theory is illustrated with
reference to natural exponential families having simple quadratic
variance function, with an application to two-way contingency
tables. We shall also deal briefly with
exponential families having homogeneous quadratic variance
function (essentially Wishart families).
This talk is based on joint work with Piero Veronese and Eduardo
Gutierrez-Pena.
The seminar will be preceded by a tutorial on Natural Exponential
Families with a view to Bayesian analysis. In particular we shall
deal with the following issues: general and natural exponential
families, variance function, alternative parameterizations,
standard conjugate families, conjugate parameterizations,
reducibility, enriched standard conjugate families.
IMPORTANTE: Il tutorial si svolgera' Venerdi' 30 aprile dalle 10.30 alle 12.00
nella Aula 1 della Facolta' di Economia.
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Elena Stanghellini
Dipartimento di Scienze Statistiche
Via A. Pascoli - C.P. 1315 Succ. 1
06100 Perugia (Italy)
Tel +39 075 5855229 or 5855242
Fax +39 075 5855950
email: elena.stanghellini@stat.unipg.it
home page: http://www.stat.unipg.it/DSS/html/elena.html
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