丸山 祐造

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.

We propose a new method of perturbing a major variable by adding noise such<br /> that results of regression analysis are unaffected. The extent of the<br /> perturbation can be controlled using a single parameter, which eases an actual<br /> perturbation application. On the basis of results of a numerical experiment, we<br /> recommend an appropriate value of the parameter that can achieve both<br /> sufficient perturbation to mask original values and sufficient coherence<br /> between perturbed and original data.