当条件分布可能不兼容时吉布斯采样器的行为。
Behavior of the Gibbs Sampler When Conditional Distributions Are Potentially Incompatible.
作者信息
Chen Shyh-Huei, Ip Edward H
机构信息
Department of Biostatistical Sciences, Wake Forest University School of Medicine, Winston-Salem, NC 27157, USA.
Department of Biostatistical Sciences, Wake Forest University School of Medicine, Winston-Salem, NC 27157, USA ; Department of Social Sciences and Health Policy, Wake Forest University School of Medicine, Winston-Salem, NC 27157, USA.
出版信息
J Stat Comput Simul. 2015;85(16):3266-3275. doi: 10.1080/00949655.2014.968159.
The Gibbs sampler has been used extensively in the statistics literature. It relies on iteratively sampling from a set of compatible conditional distributions and the sampler is known to converge to a unique invariant joint distribution. However, the Gibbs sampler behaves rather differently when the conditional distributions are not compatible. Such applications have seen increasing use in areas such as multiple imputation. In this paper, we demonstrate that what a Gibbs sampler converges to is a function of the order of the sampling scheme. Besides providing the mathematical background of this behavior, we also explain how that happens through a thorough analysis of the examples.
吉布斯采样器在统计学文献中已被广泛使用。它依赖于从一组相容的条件分布中进行迭代采样，并且已知该采样器会收敛到唯一的不变联合分布。然而，当条件分布不相容时，吉布斯采样器的行为会有很大不同。这种应用在多重填补等领域的使用越来越多。在本文中，我们证明了吉布斯采样器收敛到的结果是采样方案顺序的一个函数。除了提供这种行为的数学背景外，我们还通过对示例的深入分析来解释这种情况是如何发生的。
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