Weighted inverse gamma innovation for the structure learning of DAGs

In cancer causal analysis, graphical models can help to identify genomic changes using the relations between proteins and phosphoproteins. In particular, directed acyclic graphs (DAGs) are effective methods to analyze intricate structures of dependence and causal connections among variables. From a Bayesian standpoint, DAG structural learning is a crucial goal in genomics studies since it enables the discovery of dependent relationships that contribute to the comprehension of variable behavior. However, we benefit from Bayesian DAG learning when dealing with small sample cases such as genomics and large networks because it promotes sparsity in the graphs, integrates prior knowledge, and crucially considers the uncertainty in the graph structure. On the other hand, modeling a proper prior distribution plays a vital role in correct posterior learning. Our work recommends using a weighted prior distribution for Gaussian DAG structure learning to improve graphical metrics. Simulation studies show that our proposal is superior to the existing one. We give the network configuration using the weighted prior distribution in a cancer data analysis.