Let $X \sim N_q(\mu, \Sigma)$ with a Normal-Inverse-Wishart prior on $(\mu, \Sigma)$ i.e. $(\mu, \Sigma) \sim N_q(\mu | m, \Sigma / k) IW_q(\Sigma | \nu, \Lambda)$ where we are using the Inverse Wishart paramaterization that gives $E [\Sigma] = \frac{\Lambda^{-1}}{\nu - q -1}$.

I need the marginal distribution of $X$; I think it should be multivariate $t$ but I'm not sure. I know that if I observed $X_1, ..., X_n$ then the posterior of $\mu$ is multivariate $t$ and that the posterior predictive distribution of $X_{n+1}$ is also multivariate $t$. But I'm not so good with the calculations to get the marginal of a single $X$ under the Normal-Inverse-Wishart and I can't find it derived anywhere.

Hopefully someone knows this off the top of their head; I don't need a derivation although a reference would be good.


1 Answer 1


The marginal of a single $X$ is a student t-distribution, referring to this document: https://www.cs.ubc.ca/~murphyk/Papers/bayesGauss.pdf


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.