Minimaxity under the half-Cauchy prior

Yuzo Maruyama; Takeru Matsuda

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arXiv · 2406.08892

Minimaxity under the half-Cauchy prior

Yuzo Maruyama·Takeru Matsuda

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Abstract

This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the quadratic loss, they demonstrated that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In this paper, we theoretically establish the minimaxity of the corresponding Bayes estimator using the interval arithmetric.

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Yuzo Maruyama, Takeru Matsuda. 2024-06-13. Minimaxity under the half-Cauchy prior. https://arxiv.org/abs/2406.08892

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