# Technical Report CIS9506

 TR#: CIS9506 Class: CIS Title: A CHARACTERIZATION OF THE DIRICHLET DISTRIBUTION THROUGH GLOBAL AND LOCAL INDEPENDENCE. Authors: D. Geiger and D. Heckerman PDF CIS9506.pdf Abstract: We provide a new characterization of the Dirichlet distribution. Let $\theta_{i,j}, 1 \leq i \leq k,1 \leq j \leq n$, be positive random variables that sum to unity. Define $\theta_i = \sum^n_{j=1} \theta_{ij}, \theta_I = \{\theta_i\}^{k-1}_{i=1}, \theta_{j|i} = \theta_{ij}/\sum_j \theta_{ij}$, and $\theta_{J|i} = \{\theta_{j|i}\}^{n-1}_{j=1}$. We prove that if $\{\theta_I , \theta_{J|1},...,\theta_{J|k}\}$ are mutually independent and $\{\theta_J, \theta_{I|1},..., \theta_{I|n}\}$ are mutually independent (where $\theta_J$ and $\theta_{I|j}$ are defined analogously), and assuming strictly positive pdfs, then the pdf of $\theta_{ij}$ is Dirichlet. Copyright The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information

Remark: Any link to this technical report should be to this page (http://www.cs.technion.ac.il/users/wwwb/cgi-bin/tr-info.cgi/1995/CIS/CIS9506), rather than to the URL of the PDF files directly. The latter URLs may change without notice.