一种用于混合图模型推断的贝叶斯方法
A Bayesian Approach for Inference on Mixed Graphical Models
AI总结：
针对混合数据变量间依赖关系识别问题，提出一种满足马尔可夫性质、可处理多类数据与缺失值的贝叶斯成对图模型，结合尖峰-板条先验与MCMC算法推断，经模拟和真实进食障碍青少年数据验证有效。
摘要：
混合数据是指变量可具有多种类型（如连续型、离散型或分类型）的一类数据。这类数据在医疗保健、社会科学等多个领域被常规收集。分析此类数据的一个常见目标是识别变量间的依赖关系，以理解它们的关联。本文提出一种贝叶斯成对图模型，可估计任意类型数据间的条件独立性。我们构建了灵活的建模框架，涵盖零膨胀计数数据，还能处理缺失数据。我们证明该模型同时满足全局和局部马尔可夫性质。我们采用尖峰-板条先验（spike-and-slab prior）进行图估计，并基于条件似然实现MCMC（马尔可夫链蒙特卡洛）算法用于后验推断。我们在四种具有不同依赖结构的模拟场景（还包含随机缺失数据的情况）中评估了模型性能，并与现有方法的结果进行了比较。最后，我们对诊断为进食障碍的青少年的真实数据进行了分析。估计得到的图显示，入院时和出院时估计的关联存在差异，表明治疗可能对这些青少年的认知和行为指标产生了影响。
英文摘要：
Mixed data refers to a type of data in which variables can be of multiple types, such as continuous, discrete, or categorical. This data is routinely collected in various fields, including healthcare and social sciences. A common goal in the analysis of such data is to identify dependence relationships between variables, for an understanding of their associations. In this paper, we propose a Bayesian pairwise graphical model that estimates conditional independencies between any type of data. We implement a flexible modeling construction, that includes zero-inflated count data and can also handle missing data. We show that the model maintains both global and local Markov properties. We employ a spike-and-slab prior for the estimation of the graph and implement an MCMC algorithm for posterior inference based on conditional likelihoods. We assess performances on four simulation scenarios with distinct dependence structures, that also include cases with data missing at random, and compare results with existing methods. Finally, we present an analysis of real data from adolescents diagnosed with an eating disorder. Estimated graphs show differences in the associations estimated at intake and discharge, suggesting possible effects of the treatment on cognitive and behavioral measures in the adolescents.
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