Bayesian Inference with the von-Mises-Fisher Distribution

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In this writeup, I give an introduction to the von-Mises-Fisher (vMF) distribution which is a commonly used isotropic distribution for directional data. The writeup is an excerpt of my PhD thesis with a focus on Bayesian inference and computational considerations when working with the vMF distribution. While the initial discussion is general, some of the results and derivations for efficient inference are specialized to 3D directional data. Specifically, after the introduction of the vMF distribution and two different conjugate prior distributions, I outline general sampling from the posterior vMF distribution before deriving the normalization of the prior and the marginal data distribution for 3D. The last two sections show the cumulative density function and the entropy for the 3D vMF distribution.

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