GENERALIZED DOUBLE PARETO SHRINKAGE
GENERALIZED DOUBLE PARETO SHRINKAGE
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DOI：
10.5705/ss.2011.048
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发表时间：
2013-01-01
影响因子：
1.4
通讯作者：
Lee, Jaeyong
中科院分区：
文献类型：
--
作者：
Armagan, Artin;Dunson, David B.;Lee, Jaeyong
提出了一种广义双Pareto先验用于线性模型中的贝叶斯收缩估计和推断。先验可以通过拉普拉斯或正态分布的尺度混合来获得，从而在拉普拉斯和Normal-Jeffreys先验之间形成桥梁。虽然它像拉普拉斯密度一样在零处有尖峰，但它也有学生t形尾行为。贝叶斯计算是直接通过一个简单的吉布斯抽样算法。我们调查的最大后验估计的性质，稀疏估计在许多问题中起着重要的作用，揭示了一些完善的正则化程序的连接，并显示一些渐近结果。通过仿真和实际应用，验证了该算法的有效性。
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 t-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.