# Thread: Conditional distribution for covariance matrix with constraint

1. ## Conditional distribution for covariance matrix with constraint

Hi,

I'm trying to work out how to draw from the conditional distribution for a covariance matrix given some correlated multivariate Gaussian data.

I know the univariate distributions are all standard normal (i.e. zero mean, unit variance), so the only unknowns are the off-diagonal elements of the covariance matrix.

If it wasn't for this constraint, I could just draw from the Wishart distribution, but I'm not sure what to do with this constraint in place.

Thanks for any pointers or suggestions.

2. ## Re: Conditional distribution for covariance matrix with constraint

Do you mean you already know that the data are from a multivariate normal, with the mean vector being a zero vector and the covariance matrix has a diagonal of one?

And is it your only constraint? Or you mean other constraint? And you want to ask the distribution of the scatter matrix under this constraint, compare to the usual setting where you got the wishart distribution?

3. ## Re: Conditional distribution for covariance matrix with constraint

Originally Posted by BGM
Do you mean you already know that the data are from a multivariate normal, with the mean vector being a zero vector and the covariance matrix has a diagonal of one?
Yes that's right.

Originally Posted by BGM
And is it your only constraint? Or you mean other constraint? And you want to ask the distribution of the scatter matrix under this constraint, compare to the usual setting where you got the wishart distribution?
Yes, when I say constraint I mean the fact that the covariance matrix has ones on the diagonal. Sorry it wasn't clear.

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