  The normal-inverse-Wishart (NIW) distribution is commonly used as a prior
distribution for the mean and covariance parameters of a multivariate normal
distribution. The family of NIW distributions is also a minimal exponential
family. In this short note we describe a convergent procedure for converting
from mean parameters to natural parameters in the NIW family, or --
equivalently -- for performing maximum likelihood estimation of the natural
parameters given observed sufficient statistics. This is needed, for example,
when using a NIW base family in expectation propagation.
