Directed Acyclic Graphs (DAGs) are solid structures used to describe and infer the dependencies among variables in multivariate scenarios. Having a thorough comprehension of the accurate DAG-generating model is crucial for causal discovery and estimation. Our work suggests utilizing a non-conjugate prior for Gaussian DAG structure learning to enhance the posterior probability. We employ the idea of using the Bessel function to address the computational burden, providing faster MCMC computation compared to the use of conjugate priors. In addition, our proposal exhibits a greater rate of adaptation when compared to the conjugate prior, specifically for the inclusion of nodes in the DAG-generating model. Simulation studies demonstrate the superior accuracy of DAG learning, and we obtain the same maximum a posteriori and median probability model estimate for the AML data, using the non-conjugate prior.

翻译：有向无环图（DAG）是用于描述和推断多元场景下变量间依赖关系的稳健结构。深入理解准确的DAG生成模型对因果发现与估计至关重要。我们的研究提出在高斯DAG结构学习中采用非共轭先验以提升后验概率。通过运用贝塞尔函数解决计算负担问题，相较于共轭先验，该方法实现了更快的MCMC计算。此外，与共轭先验相比，我们的方案在DAG生成模型中节点纳入方面展现出更高的自适应速率。仿真研究表明，采用非共轭先验的DAG学习具有更优的准确性，并针对AML数据获得了相同的最大后验概率和中位数概率模型估计。