Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a multivariate Gaussian distribution with known $\mu$ and $\Sigma$. I want to evaluate it given a vector $x$. However, some of the attributes of this vector may be unknown, in which case I want to marginalize those values out.

This effectively reduces it to another MV Gaussian distribution with parameters $\hat{\mu}$ and $\hat{\Sigma}$ that are obtained after dropping the rows (and columns) corresponding to unknown attributes in $x$. (Please correct me if I am wrong).

For efficiency of implementation, I pre-compute the inverse of $\Sigma$ and determinant ($|\Sigma|$) to be used while evaluating the distribution. However, when $x$ has unknown values, is there a simple way of determining the inverse of $\hat{\Sigma}$ from the pre-computed inverse of $\Sigma$? Similarly, can I find the determinant easily for $\hat{\Sigma}$?

share|improve this question
If unsuccessful here, try stats.stackexchange.com –  user53153 Feb 12 '13 at 22:11
I was about to ask an identical question. Any suggestions appreciated. –  conjectures Feb 21 at 8:53
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.