摘要翻译：
在多向列联表的贝叶斯分析中，对数线性参数或单元概率参数的先验分布的选择是一个主要的挑战。本文对离散层次对数线性模型（包括图形模型）定义了一个灵活的共轭先验子族。这些先验被定义为在多项式抽样下受“基线约束”的对数线性参数上的Diaconis-Ylvisaker共轭先验。我们还导出了细胞概率上的诱导先验，并证明了诱导先验是超Dirichlet先验的推广。我们证明了这个先验具有几个理想的性质，并通过识别六向列联表的最可能的可分解的、图形的和层次的对数线性模型来说明它的有用性。
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英文标题：
《A conjugate prior for discrete hierarchical log-linear models》
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作者：
H\'el\`ene Massam, Jinnan Liu, Adrian Dobra
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  In Bayesian analysis of multi-way contingency tables, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameters is a major challenge. In this paper, we define a flexible family of conjugate priors for the wide class of discrete hierarchical log-linear models, which includes the class of graphical models. These priors are defined as the Diaconis--Ylvisaker conjugate priors on the log-linear parameters subject to "baseline constraints" under multinomial sampling. We also derive the induced prior on the cell probabilities and show that the induced prior is a generalization of the hyper Dirichlet prior. We show that this prior has several desirable properties and illustrate its usefulness by identifying the most probable decomposable, graphical and hierarchical log-linear models for a six-way contingency table.
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PDF链接：
https://arxiv.org/pdf/711.1609