FRIDAY, September 14, 2007
Time: 1:30 - 2:30 PM
Constant Hall 2065

Title: Generating Random Correlation Matrices Based on Partial Correlation Vines and the Onion Method

Prof. Harry Joe
Department of Statistics
University of British Columbia

Partial correlation vines and the onion method are presented for generating random correlation matrices. As a special case, a uniform distribution over the set of d X d positive definite correlation matrices obtains.

By-products are:

(a) For a uniform distribution over the space of d X d correlation matrices, the marginal distribution of each correlation is Beta (d/2,d/2) on (-1,1).

(b) An identity is obtained for the determinant of a correlation matrix R via partial correlations in a vine.

(c) A formula is obtained for the volume of the set of d X d positive definite correlation matrices in {d choose 2}-dimensional space.