Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis
Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis
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偏态分布的形状混合的贝叶斯推理及其在回归分析中的应用
DOI：
10.1214/08-ba320
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发表时间：
2008
影响因子：
4.4
通讯作者：
H. W. Gómez
中科院分区：
文献类型：
--
作者：
R. Arellano;L. M. Castro;M. Genton;H. W. Gómez
我们引入了一类具有偏态分布的形状混合，并研究了它的一些主要性质。我们讨论了所提出的类的贝叶斯解释和一些不变性结果。在模型参数的某些特殊先验条件下，我们对斜正态、斜广义正态、斜正态和斜t正态线性回归模型进行了贝叶斯分析。特别地，我们证明了在形状参数的任意适当先验和其他参数的无信息先验下，斜正态回归模型参数的全后验是适当的。为了得到相应的后验分析，我们实现了一种方便的层次表示。我们用一个关于澳大利亚男性运动员特征的真实数据集来说明我们的方法。
We introduce a class of shape mixtures of skewed distributions and study some of its main properties. We discuss a Bayesian interpretation and some invariance results of the proposed class. We develop a Bayesian analysis of the skew-normal, skew-generalized-normal, skew-normal-t and skew-t-normal linear re- gression models under some special prior specications for the model parameters. In particular, we show that the full posterior of the skew-normal regression model parameters is proper under an arbitrary proper prior for the shape parameter and noninformative prior for the other parameters. We implement a convenient hierar- chical representation in order to obtain the corresponding posterior analysis. We illustrate our approach with an application to a real dataset on characteristics of Australian male athletes.