SEMINARIO PROF. CONSONNI

[Luca Tardella <luca.tardella@uniroma1.it>]

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AVVISO DI SEMINARIO
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Il giorno venerdì 11 aprile 2003, 

alle ore 12.00, 

presso l'aula 34 (IV piano)
del Dipartimento di Statistica, Probabilità e Statistiche Applicate 
dell' Università "La Sapienza" (P.le A. Moro 5, 00185 - ROMA),

il Prof. Guido Consonni, 
dell'Università di Pavia, 

terrà un seminario dal titolo
 
"Compatible Prior Distributions for DAG
models".
 
Tutti gli interessati sono invitati a
partecipare.

Segue il riassunto del seminario.
 
Cordiali saluti

        

        

(Fulvio
De Santis)
 

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ABSTRACT
 
The application of certain Bayesian techniques,
such as the Bayes
factor and model averaging, requires the specification of prior
distributions on the parameters of alternative models. While
logically not necessary, it would seem desirable that such priors
be linked in some fashion, in order to satisfy some
'compatibility' requirement.
 
In particular we deal with 'causal' DAG
(Directed Acyclic Graph)
models which are especially appropriate whenever, in the absence
of unmeasured confounders, there exists qualitative prior
information that specifies constraints on the ordering of the
random variables under investigation. In such models, the joint
distribution of the observables is not the primitive notion, but
rather the end result of the specification of a collection of
local conditional distributions. This leads to the notion of
modular parameterisation and the characterisation of the allied
class.
 
We derive a procedure to construct compatible
priors on the
parameters of models nested within a given one using a
conditioning approach. Notable features of our method are  its
invariance within the class of modular parameterisations, as well
as the property of 'prior modularity'. Illustrations for
continuous (Gaussian) and discrete DAG models are provided.
 
The theoretical results, as well as those
related to the Gaussian
case, were developed jointly with Alberto Roverato (University of
Modena and Reggio Emilia), while the application to discrete DAGs
is collaborative work with Valentina Leucari (University of Pavia).