论文标题
稳健性的收缩：稀疏信号的对数调整的先验
Shrinkage with Robustness: Log-Adjusted Priors for Sparse Signals
论文作者
论文摘要
我们介绍了一类名为Log调整的收缩先验的新的分布，以分析稀疏信号，该分布通过将附加的日志学期乘以其密度来扩展三个参数beta先验。拟议的先验的密度尾巴比考奇分布的尾部重，并意识到贝叶斯估计量的尾巴稳定性，同时保持强烈的收缩效果对噪音。我们通过尾巴中改进的后平方误差来验证此属性。具有新密度的潜在变量的积分表示形式，并启用快速，简单的Gibbs采样器以进行完整的后验分析。我们的对数调整的先验与现有的收缩先验有显着不同，该研究的对数允许其在密度中通过多个对数字进行进一步的概括。通过模拟研究和数据分析研究了提议的先验的性能。
We introduce a new class of distributions named log-adjusted shrinkage priors for the analysis of sparse signals, which extends the three parameter beta priors by multiplying an additional log-term to their densities. The proposed prior has density tails that are heavier than even those of the Cauchy distribution and realizes the tail-robustness of the Bayes estimator, while keeping the strong shrinkage effect on noises. We verify this property via the improved posterior mean squared errors in the tail. An integral representation with latent variables for the new density is available and enables fast and simple Gibbs samplers for the full posterior analysis. Our log-adjusted prior is significantly different from existing shrinkage priors with logarithms for allowing its further generalization by multiple log-terms in the density. The performance of the proposed priors is investigated through simulation studies and data analysis.
