A discussion of prior-based Bayesian information criterion (PBIC)
A discussion of prior-based Bayesian information criterion (PBIC)
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基于先验的贝叶斯信息准则（PBIC）的讨论
DOI：
10.1080/24754269.2019.1583631
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发表时间：
2019
影响因子：
0.5
通讯作者：
Nguyen, Thuan
中科院分区：
文献类型：
--
作者：
Jiang, Jiming;Nguyen, Thuan
Bayarri教授和合著者的论文（以下简称PBIC）为已经广泛但仍在快速扩展的关于模型选择和相关主题的文献提供了一个令人鼓舞和受欢迎的补充。Müller，Scealy，and Welsh（2013）在2013年对线性混合模型中的模型选择进行了综述，作者将混合模型选择的主要方法分为三类：信息准则、收缩方法和栅栏方法。目前的文件是不是具体关于混合模型选择问题，但是，正如人们应该看到，有一个连接在各种方式。本文侧重于一个特殊情况下的信息准则，即贝叶斯信息准则（BIC）及其扩展。在这方面，除了作者引用的文献外，还可以提及另外两篇参考文献。一种是Broman和Speed（2002）的δ-BIC方法，其中调整常数δ乘以对数惩罚以提高有限样本性能;另一种是Chen和Chen（2008）提出的扩展BIC，它允许协变量的数量随着样本大小而增加。目前的文件已经注意到了一些问题，一般使用的BIC。Jiang、Rao、Gu和Nguyen（2008）在混合模型选择的背景下，不仅对BIC，而且对一般的信息标准也做了类似的说明。在这两篇论文中提到的问题是所谓的有效样本大小（ESS）。这个问题在Jiang等人的研究中自然被提出。（2008），因为后者的作者关注的是相关的观察。直观地说，当数据相关时，ESS小于观测总数，这是由于数据中的“冗余”，即每个数据点不会像独立数据点那样带来那么多的新信息。让我们来看看一个极端的情况，n个数据点是如此相关，以至于它们是相同的;显然，在这种情况下，ESS应该是1，而不是n。另一个例子，在Jiang et al.（2008）（也可参见Jiang & Nguyen，2015），是一个线性混合模型，可视为PBIC中广泛讨论的组均值模型的双向扩展。在线性混合模型中，观测值，
Professor Bayarri and coauthors’ paper (hereafter, PBIC) offers a stimulating and welcomed addition to the already extensive and yet still rapid expanding literature on model selection and related topics. In a 2013 review on model selection in linear mixed models by Müller, Scealy, and Welsh (2013), the authors classified main approaches in mixed model selection into three categories, the information criteria, the shrinkage methods and the fence methods. The current paper is not specifically regarding mixed model selection problems; however, as one shall see, there is a connection in various ways.The paper focuses on a special case of the information criteria, namely, the Bayesian information criterion (BIC) and its extensions. In this regard, two other references may be mentioned, in addition to those cited by the authors. One is the δ-BIC method of Broman and Speed (2002), in which a tuning constant, δ, is multiplied to the logarithm penalty to improve finitesample performance; the other is an extended BIC proposed by Chen and Chen (2008), which allows the number of covariates to increase with the sample size. The current paper has noted a number of problems with general use of BIC. Some similar notes were made regarding not just BIC but the information criteria in general by Jiang, Rao, Gu, and Nguyen (2008) in the context of mixed model selection. Among the problems mentioned in both papers is the so-called effective sample size (ESS). The issue was naturally raised in Jiang et al.(2008) because the latter authors were concerned with correlated observations. Intuitively, when the data are correlated, the ESS is smaller than the total number of observations due to the ‘redundancy’in the data that each data point does not bring as much new information as an independent data point. Take a look at an extreme case where n data points are so correlated that they are identical; obviously, in this case the ESS should be 1, rather than n. Another example, given in Jiang et al.(2008)(also see Jiang & Nguyen, 2015), is a linear mixed model, which may be viewed as a two-way extension of the group mean model discussed extensively in PBIC. In the linear mixed model, the observations,
影响因子：
4.5
作者：
MILLER, JJ
通讯作者：
MILLER, JJ