A method to construct exponential families by representation theory

Koichi Tojo; Taro Yoshino

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arXiv · 1811.01394

A method to construct exponential families by representation theory

Koichi Tojo·Taro Yoshino

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Abstract

In this paper, we give a method to construct "good" exponential families systematically by representation theory. More precisely, we consider a homogeneous space $G/H$ as a sample space and construct an exponential family invariant under the transformation group $G$ by using a representation of $G$. The method generates widely used exponential families such as normal, gamma, Bernoulli, categorical, Wishart, von Mises, Fisher-Bingham and hyperboloid distributions.

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Koichi Tojo, Taro Yoshino. 2018-11-04. A method to construct exponential families by representation theory. https://arxiv.org/abs/1811.01394

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