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.

翻译：我们研究了巴伊西亚程序在高维高斯低位回归时的常年性非现成性特性,如果涉及未知的骚扰参数,则要研究高斯低位回归的常年性特性。 无效参数可以是有限的、高的或无限的。 零点质量和连续分布的混合物用于先前对稀薄回归系数的分布,而适当的先前分布则用于骚扰参数。 也研究和讨论过由于存在骚扰参数而阻碍的稀薄回归系数的最佳后遗质收缩。 结果表明,该程序具有很强的模型选择一致性。 也通过可靠和有保障的常住率覆盖的组合获得了一个用于确定不确定性的Bernstein-von Mises-sorem 模型, 利用本研究中开发的理论对许多例子的无现成性特性进行了调查。