NormalInverseWishartPrior

The NormalInverseWishart distribution is a conjugate prior for the parameters of a multivariate normal distribution. Specifically, it is used as a prior for the mean vector and the covariance matrix of a multivariate normal distribution. The distribution is a combination of a normal distribution for the mean and an inverse Wishart distribution for the covariance matrix.

The NormalInverseWishart distribution is defined by four hyperparameters: a mean vector mu_0, a scalar kappa_0 which controls the confidence in the mean vector mu_0, a degrees of freedom parameter nu_0, and a scale matrix Lambda_0 for the inverse Wishart component. The multivariate normal component models the uncertainty in the mean, while the inverse Wishart component models the uncertainty in the covariance matrix.

This prior is convenient in Bayesian inference because it leads to a posterior distribution that is also of the NormalInverseWishart form. This conjugacy simplifies the computation of the posterior distribution and allows for analytical solutions in many cases. It is commonly used in applications such as regression analysis and time series modeling where uncertainty in both the mean and the spread of the data needs to be accounted for.