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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?

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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

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  • $\begingroup$ Hi @George, welcome to XV. OP seems to be asking about when conjugacy's justification goes beyond its being required or convenience. $\endgroup$ – Taylor Sep 6 '18 at 21:00

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