  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.
