Estimating the normal-inverse-Wishart distribution

TL;DR

This paper presents a convergent method for converting mean parameters to natural parameters in the normal-inverse-Wishart distribution, facilitating maximum likelihood estimation and applications like expectation propagation.

Contribution

It introduces a convergent procedure for parameter conversion in the NIW distribution, enabling more effective maximum likelihood estimation.

Findings

Provides a stable method for parameter conversion in NIW distributions

Enables efficient maximum likelihood estimation of natural parameters

Supports applications such as expectation propagation

Abstract

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.