论文标题
统一的贝叶斯稀疏线性回归理论，具有滋扰参数
Unified Bayesian theory of sparse linear regression with nuisance parameters
论文作者
论文摘要
当涉及未知的滋扰参数时，我们研究了贝叶斯程序的频繁渐近性能，用于高维高斯稀疏回归。滋扰参数可以是有限的，高或无限的。点质量为零的混合物，并将连续分布用于稀疏回归系数上的先验分布，并将适当的先验分布用于滋扰参数。还检查和讨论了稀疏回归系数的最佳后验收缩，受到滋扰参数的影响。结果表明，该过程产生强大的模型选择一致性。还通过可靠的频繁覆盖范围可靠的集合获得了不确定性定量的稀疏回归系数的伯恩斯坦 - 冯·梅斯型定理。使用本研究中开发的理论研究了许多例子的渐近特性。
We study frequentist asymptotic properties of Bayesian procedures for high-dimensional Gaussian sparse regression when unknown nuisance parameters are involved. Nuisance parameters can be finite-, high-, or infinite-dimensional. A mixture of point masses at zero and continuous distributions is used for the prior distribution on sparse regression coefficients, and appropriate prior distributions are used for nuisance parameters. The optimal posterior contraction of sparse regression coefficients, hampered by the presence of nuisance parameters, is also examined and discussed. It is shown that the procedure yields strong model selection consistency. A Bernstein-von Mises-type theorem for sparse regression coefficients is also obtained for uncertainty quantification through credible sets with guaranteed frequentist coverage. Asymptotic properties of numerous examples are investigated using the theories developed in this study.
