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）分布通常用作多元正态分布均值与协方差参数的先验分布。NIW分布族同时也是最小指数族。本短讯描述了一种在NIW分布族中将均值参数转换为自然参数的收敛计算流程，等价而言——即根据观测充分统计量进行自然参数的最大似然估计。例如在期望传播算法中使用NIW基础分布族时，此类计算具有必要性。