Avviso di Seminario - Universita' di Pavia

["Leonardo Bottolo" <lbottolo@eco.unipv.it>]

UNIVERSITA' DEGLI STUDI DI PAVIA
DIPARTIMENTO DI ECONOMIA POLITICA E METODI QUANTITATIVI
DIPARTIMENTO DI MATEMATICA "F.CASORATI"
DOTTORATO DI RICERCA IN MATEMATICA E STATISTICA
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                        AVVISO DI SEMINARIO


Giovedi' 27 febbraio, alle ore 15.00, nell'aula del Consiglio di Facolta',
Dipartimento di Economia Politica e Metodi Quantitativi (via San Felice 5,
Pavia)


                          ALBERTO ROVERATO
    (Dipartimento di Scienze Sociali, Cognitive e Quantitative
                 Univerita' di Modena e Reggio Emilia)


terra' un seminario dal titolo:


        A UNIFIED APPROACH TO THE CHARACTERISATION OF
            EQUIVALENCE CLASSES OF DAGS, CHAIN GRAPHS
                      WITH NO FLAGS AND CHAIN GRAPHS



Abstract:

A Markov property associates a set of conditional independencies to a
graph. Two alternative Markov properties are available for chain graphs,
the LWF and the AMP Markov property, which are different in general but
coincide for the subclass of chain graphs with no flags. Markov
equivalence induces a partition of the class of chain graphs into
equivalence classes and every equivalence class contains a, possibly
empty, subclass of chain graphs with no flags itself containing a,
possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov
equivalence classes of chain graphs can be naturally characterised by
means of the so-called largest chain graphs whereas a graphical
characterisation of equivalence classes of DAGs is provided by the
essential graphs. In this work we show the existence of largest chain
graphs with no flags that provide a natural characterisation of
equivalence classes of chain graphs with respect to both the LWF and
the AMP Markov properties. We propose a procedure for the construction
of the largest chain graph, the largest chain graph with no flags and
the essential graph, thereby providing a unified approach to the problem.
As a by-product we obtain a characterisation of the largest chain graph
with no flags and an alternative characterisation of the largest chain
graph. Furthermore, a known characterisation of the essential graph is
shown to be a special case of our more general framework. The three
graphical characterisations are based on a common set of rules and allow
an immediate comparison of the three characterising graphs.




Durante il seminario sarà offerto ai partecipanti un piccolo rinfresco.


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Per ulteriori informazioni riguardo ai Seminari di Probabilita' e
Statistica e' possibile scrivere a:

lbottolo@eco.unipv.it

oppure consultare la pagina WEB dei seminari:

http://economia.unipv.it/eco-pol/semstat/semstat.htm