# Estimating the normal-inverse-Wishart distribution

arXiv: https://arxiv.org/abs/2405.16088 · HTML: https://mlsanity.com/paper/2405.16088/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 3 references that are in the map.
- First posted on arXiv 25 May 2024.

## Built on by (most cited first, 2 of 2)

- [Fearless Stochasticity in Expectation Propagation](https://mlsanity.com/paper/2406.01801/) (2024)
- [Converge to Surprise: Evolutionary Self-supervised Image Clustering](https://mlsanity.com/paper/2607.06887/) (2026)

## Abstract (arXiv)

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.