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缩小肩膀的收缩:吉布斯采样收缩模型后部,有保证的收率

Akihiko Nishimura¹, Marc A Suchard²

¹Department of Biostatistics, Johns Hopkins University Bloomberg School of Public Health.

Bayesian analysis

|May 21, 2024

概括

这项研究引入了缩先验的新型规范化方法,增强了稀疏贝叶斯推理的稳定性. 该方法确保稳定的参数估计,即使数据提供弱的识别,提高计算效率.

科学领域:

统计统计统计统计
计算统计学计算统计学
贝叶斯的推理是贝叶斯的推理.

背景情况:

连续收缩先验对于诱导参数估计中的稀疏性很受欢迎.
识别得不清楚的参数可能会导致重的后尾,损害推断的稳定性.
现有的规范化方法可能会改变收缩先验的计算特性.

研究的目的:

开发一个规范化方法,以保持计算优势的收缩先验.
分析基布斯采样器对规则化的收缩先验的理论性质.
在稀疏后勤回归中调查Pólya-Gamma Gibbs采样器的收率.

主要方法:

开发一种规范化技术,以"缩小肩膀"的缩小先行者.
分析基布斯样本的几何ergodicity,以调整后部分布.
在特定条件下研究前者的局部尺度参数的收性质.

主要成果:

拟议的规范化保留了原始收缩先验的计算上有吸引力的结构.
这种规范化导致了对广泛的全球-本地收缩先验的几何厄戈迪性.
在特定的条件下 (例如,贝叶斯桥 priors),可以证明采样器的均ergodicity.

结论:

开发的规范化方法提高了稀疏贝叶斯推理的稳定性,而不会牺牲计算效率.
理论分析为使用的吉布斯样本与这些规范化先验的收提供了保证.
这项工作为统计应用中可靠的稀疏建模提供了有价值的工具.

关键词:

贝叶斯的推理贝叶斯的推理马尔科夫连锁蒙特卡罗的蒙特卡罗是一个主要的 60J20,62F1515 的情况.侵蚀性侵蚀性侵蚀性一般化的线性模型.二次性 62J07 一次性的稀缺性是一种稀缺性.

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