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.

翻译：正态-逆威沙特（NIW）分布通常作为多元正态分布均值与协方差参数的先验分布使用。NIW分布族同时也是最小指数族。本短文提出了一种收敛算法，用于实现NIW分布族中均值参数向自然参数的转换，或者等价地——在给定观测充分统计量的条件下执行自然参数的最大似然估计。该算法在期望传播中使用NIW基础分布族等场景中具有重要应用价值。