标题： 针与草垛：可能稀疏序列的后验集中性 显示英文标题

标题： Needles and Straw in a Haystack: Posterior concentration for possibly sparse sequences

摘要： 我们考虑多元正态均值模型中的全贝叶斯推断问题，其中均值向量是稀疏的。 通过首先选择一组非零均值，然后对这些非零值赋予先验分布，构建均值向量上的先验分布。 我们在观察值由固定均值向量生成的频率学派框架下研究后验分布，并关注非零分量个数的后验分布以及后验分布收敛到真实均值向量的速度。 我们发现多种先验组合，它们在非零系数个数和这些系数上具有理想性能。 我们也找到一些导致次优收敛速度的先验，例如，非零系数上的高斯先验。 我们通过模拟验证了这些结果。 显示英文摘要

摘要： We consider full Bayesian inference in the multivariate normal mean model in the situation that the mean vector is sparse. The prior distribution on the vector of means is constructed hierarchically by first choosing a collection of nonzero means and next a prior on the nonzero values. We consider the posterior distribution in the frequentist set-up that the observations are generated according to a fixed mean vector, and are interested in the posterior distribution of the number of nonzero components and the contraction of the posterior distribution to the true mean vector. We find various combinations of priors on the number of nonzero coefficients and on these coefficients that give desirable performance. We also find priors that give suboptimal convergence, for instance, Gaussian priors on the nonzero coefficients. We illustrate the results by simulations.