1
$\begingroup$

I am trying to understand what is going on in the use of an Inverse Wishart prior for (Gaussian) covariance, and what is the motivation for it. I am seeing this posed as a solution for when the parameters being estimated do not have sufficiently many data samples to be estimated from.

I have looked a little in Murphy's book and Bishop's but I feel they are diving too quickly into technical details, leaving me in the dust. Any explanation or suggested reading is much appreciated.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
3
$\begingroup$

I assume you are aware that Wishart matrices can be generated as the outer product $X^TX$ of a matrix where each row is an independent observation of a multivariate normal distribution, yes? So a Wishart prior might emerge from an assumption of multivariate normality in your data. The inverse Wishart is the distribution of the inverse of these outer products and is therefore also a distribution over SPD matrices. Choosing the inverse Wishart as prior guarantees a nice form for the posterior, but intuitively the Wishart is also a decent choice with the added benefit of not inversely penalizing matrices with large determinants.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.