Bayesian Methods for Generalized Linear Models
Bayesian Methods for Generalized Linear Models
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发表时间：
1999
影响因子：
0.4
通讯作者：
P. Green;Daehak Kim
中科院分区：
文献类型：
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作者：
P. Green;Daehak Kim
广义线性模型对于来自多种统计研究的数据有各种应用。虽然响应变量通常被假设为从一个广泛的概率分布类生成，我们专注于计数数据，最常用的比例或泊松模型的比例分析。由于多项式和泊松抽样之间的关系，本文给出的方法和结果也适用于许多其他分类数据模型。这里建议的方法的新奇是，所有的条件分布s可以直接指定，使staraightforward吉布斯采样是可能的。先验分布由两个阶段组成。我们依赖于一个正常的非共轭先验在第一阶段和一个模糊的先验超参数在第二阶段。使用Rosenkranz和raftery（1994）收集的有关华盛顿州因背痛住院人数的数据，通过一个说明性示例来演示这些方法。
Generalized linear models have various applications for data arising from many kinds of statistical studies. Although the response variable is generally assumed to be generated from a wide class of probability distributions we focus on count data that are most often analyzed using binomial models for proportions or poisson models for rates. The methods and results presented here also apply to many other categorical data models in general due to the relationship between multinomial and poisson sampling. The novelty of the approach suggested here is that all conditional distribution s can be specified directly so that staraightforward Gibbs sampling is possible. The prior distribution consists of two stages. We rely on a normal nonconjugate prior at the first stage and a vague prior for hyperparameters at the second stage. The methods are demonstrated with an illustrative example using data collected by Rosenkranz and raftery(1994) concerning the number of hospital admissions due to back pain in Washington state.