Minimaxity under half-Cauchy type priors

Yuzo Maruyama; Takeru Matsuda

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arXiv · 2308.09339

Minimaxity under half-Cauchy type priors

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 normal mean vector under the quadratic loss, they showed that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In terms of the shrinkage coefficient, the half-Cauchy prior has a U-shape and can be interpreted as a continuous spike and slab prior. In this paper, we consider a general class of priors with U-shapes and theoretically establish sufficient conditions for the minimaxity of the corresponding (generalized) Bayes estimators. We also develop an algorithm for posterior sampling and present numerical results.

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Yuzo Maruyama, Takeru Matsuda. 2023-08-18. Minimaxity under half-Cauchy type priors. https://arxiv.org/abs/2308.09339

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