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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1$\begingroup$ I would suggest stats.stackexchange.com/questions/155059/… for consideration $\endgroup$– beuhbbbCommented Aug 8, 2017 at 15:28
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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
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1$\begingroup$ Hi @George, welcome to XV. OP seems to be asking about when conjugacy's justification goes beyond its being required or convenience. $\endgroup$– TaylorCommented Sep 6, 2018 at 21:00