no subject (file transmission)

[Giovanni Sebastiani <sebast@iac.rm.cnr.it>]

                Avviso di corso di dottorato: 



                 Gaussian graphical models


                    Prof. Gerard Letac

                Universite'  Paul Sabatier
                     Toulouse, France

  
  
              Universita' di Roma "La Sapienza"
   Dipartimento di Matematica Istituto "Guido Castelnuovo" 
Aula B, Tuesday and Wednesday, 14:00 - 16:00, Nov. 8 - Dec. 14
                 
                         
                            Program
 
November 8th, Tuesday. Simpson paradox. Discrete
graphical models. A refreshment about Gaussian distributions in
$\mathbb{R}^n$ and the estimation of their parameters.

November 9th, Wednesday. Dempster models.
Why estimation by maximum likelihood is impossible if the graph is
not decomposable. The two fundamental cones $P_G$ and $Q_G$ of a
decomposable graph.

November 15th, Tuesday. The geometry of the decomposable graphs: the
maximal cliques, the minimal separators and their multiplicities.

November 16th, Wednesday. Examples of decomposable graphs: $A_n$, 
daisies, trees, homogeneous graphs.

November 22th, Tuesday. The Gavril Buneman theorem:
every decomposable graph is a graph of subtrees of a tree.

November 23th, Wednesday. Perfect ordering of the
vertices, perfect ordering of the maximal cliques of a
decomposable graph.

November 29th, Tuesday. The Lauritzen's magical formula for a
decomposable graph. Application to the duality between the two
cones $P_G$ and $Q_G.$

November 30th, Wednesday. A refreshment on the
classical Wishart distribution. The Dawid-Lauritzen and the
Roverato distributions for a decomposable graph.

December 6th, Tuesday. The Wishart distributions of
type I and II for a decomposable graph. The eigenvalue property.
The case of homogeneous graphs.

December 7th, Wednesday. The Wishart distributions of
type I and II for a decomposable graph: the non homogeneous case.
Explicit computation for $A_4.$

December 13th, Tuesday. An elementary look on the real homogeneous
cones and their use in statistics (S. Andersson's theory).

December 14th, Wednesday. Wishart distributions of type
I and II and their use in Bayesian estimation. Their hyperMarkov
properties.

  
            For more information, please contact: 
   Prof. Mauro Piccioni (e-mail: piccioni@mat.uniroma1.it)



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