When I try to calculate the Information matrix of a multivariate Gaussian of dimension d, I arrive at
I(Sigma) = 0.5 * D' * kron( Sigma^(-1), Sigma^(-1) ) * D where D is the duplication matrix, Sigma is the covariance matrix of the Gaussian, kron is the kronecker product. (I hope I do not make a mistake in my calculation... but I am not sure.) I am wondering if the integral int D' * kron( Sigma^(-1), Sigma^(-1) ) * D ds is finite or not, where vec Sigma = D s To make the matter worse, I do not know how to state the integration limit, since the integration should be over values of s that make Sigma positive definite. My guess is that the integral is infinite, since Jeffery's prior is usually improper. If my guess is correct, does close form solution exist for the integral if the range of the integration is restricted to a bounded subset? The form of the subset is not important, since I am trying to modify the prior to become "proper". Any pointers or references are welcome, as this is the first time I handle matrix parameter. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
