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arXiv · 1612.07946

Bayes estimator for multinomial parameters and Bhattacharyya distances

Christopher Ferrie·Robin Blume-Kohout
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Abstract

We derive the Bayes estimator for the parameters of a multinomial distribution under two loss functions ($1-B$ and $1-B^2$) that are based on the Bhattacharyya coefficient $B(\vec{p},\vec{q}) = \sum{\sqrt{p_kq_k}}$. We formulate a non-commutative generalization relevant to quantum probability theory as an open problem. As an example application, we use our solution to find minimax estimators for a binomial parameter under Bhattacharyya loss ($1-B^2$).

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Christopher Ferrie, Robin Blume-Kohout. 2016-12-23. Bayes estimator for multinomial parameters and Bhattacharyya distances. https://arxiv.org/abs/1612.07946

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