标题： 结构收缩先验 显示英文标题

标题： Structured Shrinkage Priors

摘要： 在许多回归设置中，未知系数可能具有一些已知结构，例如它们可能在空间上有序，或者对应于向量化矩阵或张量。 同时，未知系数可能是稀疏的，其中许多接近于零或恰好为零。 然而，许多常用的系数先验和相应的惩罚项并不鼓励同时具有结构和稀疏性的估计。 在本文中，我们开发了结构收缩先验，这些先验推广了多元正态、拉普拉斯、指数幂和正态-伽马先验。 这些先验允许回归系数在先验上相关，而不会牺牲逐元素的稀疏性或收缩。 在使用这些结构收缩先验时，主要挑战是计算上的，因为相应的惩罚项是难以处理的积分，且为了近似后验众数或从后验分布中抽样所需的全条件分布可能是非标准的。 我们通过使用一种灵活的椭圆切片抽样程序来克服这些问题，并证明这些先验可以在保持稀疏性的同时引入结构。 显示英文摘要

摘要： In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with many nearly or exactly equal to zero. However, many commonly used priors and corresponding penalties for coefficients do not encourage simultaneously structured and sparse estimates. In this paper we develop structured shrinkage priors that generalize multivariate normal, Laplace, exponential power and normal-gamma priors. These priors allow the regression coefficients to be correlated a priori without sacrificing elementwise sparsity or shrinkage. The primary challenges in working with these structured shrinkage priors are computational, as the corresponding penalties are intractable integrals and the full conditional distributions that are needed to approximate the posterior mode or simulate from the posterior distribution may be non-standard. We overcome these issues using a flexible elliptical slice sampling procedure, and demonstrate that these priors can be used to introduce structure while preserving sparsity.