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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