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Inverse Wishart (which is used in the mentioned article) is used as a prior for the covariance matrix of a multivariate Normal distributed random variable. This choice is based on the fact that its a conjugate prior for the covariance matrix in this scenario. If $\mathbf{X}=(\mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_n) \sim \mathcal{N}(\mathbf{0}, \...


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