Solved – Normal-inverse-Wishart distribution

Question

The Normal-inverse-Wishart distribution is a conjugate prior for the multivariate normal distribution when the mean and covariance are unknown. I understand that conjugate priors are mathematically convenient but are there specific applications where the justification for using the Normal-inverse-Wishart distribution prior goes beyond convenience?

Answer 1

One application is the Gibbs Sampling from a Dirichlet Process mixture model, where a conjugate prior is required. See page 33 of the pdf below

https://www.cs.cmu.edu/~kbe/dp_tutorial.pdf