Armagan Artin, Dunson David B, Lee Jaeyong
SAS Institute Inc., Durham, NC 27513, USA,
Department of Statistical Science, Duke University, Durham, NC 27708, USA,
Stat Sin. 2013 Jan 1;23(1):119-143.
We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it also has a Student's -like tail behavior. Bayesian computation is straightforward via a simple Gibbs sampling algorithm. We investigate the properties of the maximum a posteriori estimator, as sparse estimation plays an important role in many problems, reveal connections with some well-established regularization procedures, and show some asymptotic results. The performance of the prior is tested through simulations and an application.
我们提出了一种用于贝叶斯收缩估计和线性模型推断的广义双帕累托先验。该先验可通过拉普拉斯分布或正态分布的尺度混合得到，在拉普拉斯先验和正态 - 杰弗里斯先验之间架起了一座桥梁。虽然它像拉普拉斯密度一样在零处有一个尖峰，但也具有类似学生分布的尾部行为。通过简单的吉布斯采样算法，贝叶斯计算很直接。我们研究了最大后验估计器的性质，因为稀疏估计在许多问题中起着重要作用，揭示了与一些成熟正则化程序的联系，并展示了一些渐近结果。通过模拟和一个应用测试了该先验的性能。
