论文标题
马蹄形的拉普拉斯混合物表示和一些含义
A Laplace Mixture Representation of the Horseshoe and Some Implications
论文作者
论文摘要
马蹄提前定义为正常的半牛chy尺度混合物，为贝叶斯稀疏信号恢复提供了最先进的方法。我们提供了马蹄密度作为拉普拉斯密度的比例混合物的新表示，明确识别混合度量。使用著名的伯恩斯坦（Widder Theorem）和由于Bochner的结果，我们的代表立即确立了马蹄密度的完全单调性和相应罚款的强烈凹度。因此，建立了局部线性近似和期望之间的等效性 - 在马蹄形惩罚回归下找到后验模式的最大化算法。此外，结果估计显示稀疏。
The horseshoe prior, defined as a half Cauchy scale mixture of normal, provides a state of the art approach to Bayesian sparse signal recovery. We provide a new representation of the horseshoe density as a scale mixture of the Laplace density, explicitly identifying the mixing measure. Using the celebrated Bernstein--Widder theorem and a result due to Bochner, our representation immediately establishes the complete monotonicity of the horseshoe density and strong concavity of the corresponding penalty. Consequently, the equivalence between local linear approximation and expectation--maximization algorithms for finding the posterior mode under the horseshoe penalized regression is established. Further, the resultant estimate is shown to be sparse.
