Bayesian finite mixtures of Ising models

IF 0.9 4区 数学 Q3 STATISTICS & PROBABILITY Metrika Pub Date : 2024-05-20 DOI:10.1007/s00184-024-00970-4
Zhen Miao, Yen-Chi Chen, Adrian Dobra
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Abstract

We introduce finite mixtures of Ising models as a novel approach to study multivariate patterns of associations of binary variables. Our proposed models combine the strengths of Ising models and multivariate Bernoulli mixture models. We examine conditions required for the local identifiability of Ising mixture models, and develop a Bayesian framework for fitting them. Through simulation experiments and real data examples, we show that Ising mixture models lead to meaningful results for sparse binary contingency tables with imbalanced cell counts. The code necessary to replicate our empirical examples is available on GitHub: https://github.com/Epic19mz/BayesianIsingMixtures.

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伊辛模型的贝叶斯有限混合物
我们引入了有限伊辛混合物模型,作为研究二元变量多变量关联模式的一种新方法。我们提出的模型结合了伊辛模型和多元伯努利混合物模型的优点。我们研究了 Ising 混合物模型局部可识别性所需的条件,并开发了拟合这些模型的贝叶斯框架。通过模拟实验和真实数据示例,我们证明了 Ising 混合物模型可以为具有不平衡单元格数的稀疏二元或然表带来有意义的结果。复制我们的经验示例所需的代码可在 GitHub 上获取:https://github.com/Epic19mz/BayesianIsingMixtures。
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来源期刊
Metrika
Metrika 数学-统计学与概率论
CiteScore
1.50
自引率
14.30%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Metrika is an international journal for theoretical and applied statistics. Metrika publishes original research papers in the field of mathematical statistics and statistical methods. Great importance is attached to new developments in theoretical statistics, statistical modeling and to actual innovative applicability of the proposed statistical methods and results. Topics of interest include, without being limited to, multivariate analysis, high dimensional statistics and nonparametric statistics; categorical data analysis and latent variable models; reliability, lifetime data analysis and statistics in engineering sciences.
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