conjugate prior (and posterior) for Matrix Variate Distributions

I was wondering what is the conjugate prior for Matrix Variate Distributions (e.g., unknown mean, known variance matrices), and what's the corresponding posterior? Is there analytical solution?

• First of all, for any probability distribution belonging to the exponential family, (such as, Gamma family, Gaussian, Poisson, Binomial, Double exponential, F, t, .......), we have their conjugate prior inside the exponential family. Your question is, for Matrix Variate Distributions, (I suppose the Wishart Distribution corresponds to multi-dimensional chi-square, Matrix variate Dirichlet distribution), is there analytical solution. I wanna say yes here provided that your distribution itself belongs to the exponential family. Hope it helps you a little bit. – son520804 Jan 23 '18 at 1:43
• @son520804 Thanks a lot! I will read more about exponential family. – user3138073 Jan 24 '18 at 20:30
• To elaborate, I want to say that exponential family is not restricted to single parameter model, but extended to the multivariate models, so we still get analytical solution. In case of having strange distributions that does not belong to the exponential family, we typically do not have analytical solution and will do the Gibbs' sampling, which is a programming tool that you may read in this section. – son520804 Jan 24 '18 at 20:50
• which matrix variate distribution? – Taylor Jul 22 '18 at 18:14