The Polya-Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic
The Polya-Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic
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DOI：
10.1214/13-ejs837
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发表时间：
2013-01-01
影响因子：
1.1
通讯作者：
Hobert, James P.
中科院分区：
文献类型：
--
作者：
Choi, Hee Min;Hobert, James P.
最广泛使用的数据增强算法之一是Albert和Chibs（1993）贝叶斯概率回归算法。Polson，Scott和Windle（2013）最近介绍了贝叶斯逻辑回归的类似算法。两者之间的主要区别是Albert和Chibs（1993）截断的法线被所谓的Polya-Gamma随机变量所取代。在本文中，我们建立了Polson，Scott和Windles（2013）算法的马尔可夫链是一致遍历的。这一理论结果具有重要的实际意义。特别是，它保证了中心极限定理的存在，可以用来做出明智的决定，多长时间的模拟应该运行。
One of the most widely used data augmentation algorithms is Albert and Chibs (1993) algorithm for Bayesian probit regression. Polson, Scott, and Windle (2013) recently introduced an analogous algorithm for Bayesian logistic regression. The main difference between the two is that Albert and Chibs (1993) truncated normals are replaced by so-called Polya-Gamma random variables. In this note, we establish that the Markov chain underlying Polson, Scott, and Windles (2013) algorithm is uniformly ergodic. This theoretical result has important practical benefits. In particular, it guarantees the existence of central limit theorems that can be used to make an informed decision about how long the simulation should be run.