双高斯DAG-probit模型中的贝叶斯因果推断
Bayesian Causal Inference in Doubly Gaussian DAG-probit Models
AI总结：
本文提出双高斯DAG-probit模型，在共享部分参数的前提下为两组观测数据分别构建有向无环图，并通过MCMC后验采样估计DAG骨架、节点效应大小及模型参数，模拟与真实数据实验验证了分组变量在因果推断中的价值。
摘要：
我们考虑在观测数据下对两个组的二元响应变量及一组协变量进行建模。分组变量可以是混杂变量（处理与结果的共同原因）、性别、病例/对照、种族等。给定协变量和一个二元潜变量，目标是在共享一些公共参数的同时构建两个有向无环图（DAG）。代表变量的节点集合对两组是相同的，但代表变量之间因果关系的节点间有向边可能不同。对于每个组，我们还估计每个节点的效应大小。我们假设每个组在其DAG下服从高斯分布。给定父节点，由于DAG的马尔可夫性质，DAG的联合分布是条件独立的。我们引入两组下的高斯DAG-probit模型概念，从而提出双高斯DAG-probit模型。为了估计DAG的骨架和模型参数，我们通过MCMC方法从双高斯DAG-probit模型的后验分布中采样。我们使用全面的模拟实验验证了所提出的方法，并将其应用于两个真实数据集。此外，我们使用著名的实验研究验证了真实数据分析的结果，以展示所提出的分组变量在因果领域中的价值。
英文摘要：
We consider modeling a binary response variable together with a set of covariates for two groups under observational data. The grouping variable can be the confounding variable (the common cause of treatment and outcome), gender, case/control, ethnicity, etc. Given the covariates and a binary latent variable, the goal is to construct two directed acyclic graphs (DAGs), while sharing some common parameters. The set of nodes, which represent the variables, are the same for both groups but the directed edges between nodes, which represent the causal relationships between the variables, can be potentially different. For each group, we also estimate the effect size for each node. We assume that each group follows a Gaussian distribution under its DAG. Given the parent nodes, the joint distribution of DAG is conditionally independent due to the Markov property of DAGs. We introduce the concept of Gaussian DAG-probit model under two groups and hence doubly Gaussian DAG-probit model. To estimate the skeleton of the DAGs and the model parameters, we took samples from the posterior distribution of doubly Gaussian DAG-probit model via MCMC method. We validated the proposed method using a comprehensive simulation experiment and applied it on two real datasets. Furthermore, we validated the results of the real data analysis using well-known experimental studies to show the value of the proposed grouping variable in the causality domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
