[Forum SIS] Bocconi DEC Seminar: R. Ramamoorthi - May 10th

[anna.simoni a unibocconi.it]

Dear colleagues, 



The Department of Decision Sciences (DEC) of Bocconi University is pleased to invite you to the seminar: 

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DEC Seminar 
Università Bocconi, 
Room 33 
Via Sarfatti 25 - 3rd floor 
Time: 12:30pm 

The DEC seminar schedule is available at http://www.unibocconi.eu/statseminar 

Monday, May 10th 

Ramanathapuram Ramamoorthi 
(Michigan State University) 

"On a Characterization of Dirichlet Distribution " 

Abstract: 

Let Z = (X, Y ) be a random variable taking values in a finite set 
I×J. For any distribution P on I×J, let P(•) be the marginal distribution of X 
and let P•|i be the conditional distribution of Y given X = i. Define Q(•),Q•|j 
be the marginal and conditional distribution of Y and X given Y = j. Geiger 
and Heckerman[The Annals of Statistics, Vol. 25, No. 3. (Jun., 1997), pp. 
1344-1369.] showed that if a prior II for the distribution of Z, satisfies, under II, 
(1) P(•) is independent of {P•|i : i Є I} and 
(2) {P•|j Є j 2 J} are independent among themselves 
(3) a similar statement holds for Q•,Q•|j 
then II is a Dirichlet distribution. 
We provide a simpler proof of the above characterization. Then we indicate 
an extension of the result to general Dirichlet process and also examine the 
distribution of the conditional distribution P|X for a general Dirichlet process. 
This is joint work with Laura Sangalli. 

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Sincerely, 
Anna Simoni 

-- --------------------------- 
Anna Simoni 

Assistant Professor 
Department of Decision Sciences 
Università Bocconi 
via Roentgen, 1 
20136 Milano - Italy 

Email:anna.simoni a unibocconi.it 
Webpage: http://faculty.unibocconi.eu/annasimoni/ 


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