 If the observations formula_40 are independent p-variate Gaussian variables drawn from a formula_41 distribution, then the conditional distribution formula_42 has a formula_43 distribution, where formula_44.Because the prior and posterior distributions are the same family, we say the inverse Wishart distribution is conjugate to the multivariate Gaussian.Due to its conjugacy to the multivariate Gaussian, it is possible to marginalize out (integrate out) the Gaussian's parameter formula_45.