Minimaxity under the half-Cauchy prior

Yuzo Maruyama and Takeru Matsuda

Journal of Multivariate Analysis, 2025, vol. 208, issue C

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 arithmetic.

Keywords: Half-Cauchy prior; Interval arithmetic; Minimaxity; Spike and slab prior (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2025.105431

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