We propose tractable symmetric exponential families of distributions for multivariate vectors of 0's and 1's in dimensions, or what are referred to in this paper as binary vectors, that allow for nontrivial amounts of variation around some central value . We note that more or less standard asymptotics provides likelihood-based inference in the one-sample problem. We then consider mixture models where component distributions are of this form. Bayes analysis based on Dirichlet processes and Jeffreys priors for the exponential family parameters prove tractable and informative in problems where relevant distributions for a vector of binary variables are clearly not symmetric. We also extend our proposed Bayesian mixture model analysis to datasets with missing entries. Performance is illustrated through simulation studies and application to real datasets.

中文翻译：

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具有二进制坐标的向量的维数分布的简单对称指数族混合的建模和推理

我们为维数为 0 和 1 的多元向量或本文中称为二元向量的多变量向量提出了易于处理的对称指数分布族，它允许围绕某个中心值发生非平凡的变化量. 我们注意到或多或少的标准渐近法在单样本问题中提供了基于似然的推理。然后我们考虑混合模型，其中组件分布具有这种形式。基于狄利克雷过程和指数族参数的杰弗里斯先验的贝叶斯分析在二元变量向量的相关分布明显不对称的问题中证明是易于处理和提供信息的。我们还将我们提出的贝叶斯混合模型分析扩展到缺少条目的数据集。通过模拟研究和对真实数据集的应用来说明性能。