Avviso di seminario

["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 STATISTICA MATEMATICA
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                         AVVISO DI SEMINARIO


Lunedi' 28 maggio, alle ore 16.00, nell'aula G del Dipartimento di
Economia Politica e Metodi Quantitativi (via San Felice 5, Pavia)


                          CLAUDIA TARANTOLA
      (Dipartimento di Economia Politica e Metodi Quantitativi,
                  Universita' degli Studi di Pavia)


terra' un seminario dal titolo:


                  SPANNING TREES E MODELLI GRAFICI



Riassunto.

In the study of graphical model it is sometimes useful to detect if the
examined graph contains cyclic structures. We shall consider two
different situations: identifiable graphical single factor models and
decomposable graphical models.
In the analysis of graphical single factor models it is fundamental to
look for odd cycles in the complementary graph of the residual. In fact,
only if the complementary graph of the residuals contains at least one
odd cycle the model is identifiable, see Stanghellini (1997) and Vicard
(2000).
On the other hand working with decomposable models, we are interested in
any chordless cycle of length equal or greater than 4; in fact a graph
is decomposable if and only if it is triangulated (see e.g. Lauritzen,
1995).
We shall show how the spanning tree, i.e. a particular tree sub-graph of
a given graph, permits to detect in an efficient way the presence of
cyclic structures in the considered graph. More precisely, the spanning
tree permits to identify a base of the space of all cycles, the set of
fundamental cycles. All the other cycles of the graph can be expressed
as a linear combination of the fundamental ones using the operation of
ring sum.
We shall at first present an efficient algorithm that can be used for
the identifiable case, see Tarantola and Vicard (2000) and then we shall
present a novel methodology for the decomposable case.




Durante il seminario sarà offerto ai partecipanti un piccolo rinfresco.


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