This paper presents a method for learning Bayesian networks that combines user knowledge with statistical data. The authors identify two key properties of scoring metrics: event equivalence and parameter modularity. Event equivalence ensures that two Bayesian networks representing the same independence assertions receive the same score, while parameter modularity allows for the independent treatment of parameters in different network structures. These properties simplify the encoding of user knowledge and enable the combination of prior knowledge with statistical data. The paper discusses the use of Bayesian principles to develop algorithms that take user knowledge (expressed as a prior Bayesian network) and statistical data as inputs, and return improved Bayesian networks. It describes the scoring metric for belief networks, which is similar to existing metrics but scores directed networks rather than undirected ones. The authors also introduce the concept of event equivalence, which is crucial for ensuring that isomorphic belief networks receive the same score. The paper introduces the BDe metric, a score-equivalent metric for belief networks that incorporates a prior belief network and an equivalent sample size. This metric allows for the combination of user knowledge and statistical data, and is shown to exhibit score equivalence. The BDe metric is evaluated on the Alarm network, demonstrating its effectiveness in learning Bayesian networks from data. The paper also discusses the limitations of the BDe metric, particularly in cases where the prior knowledge is not accurate or complete. It suggests that while score equivalence is important, other assumptions such as Dirichlet priors may be relaxed in certain situations. The authors conclude that the BDe metric provides a powerful tool for learning Bayesian networks from a combination of user knowledge and statistical data.This paper presents a method for learning Bayesian networks that combines user knowledge with statistical data. The authors identify two key properties of scoring metrics: event equivalence and parameter modularity. Event equivalence ensures that two Bayesian networks representing the same independence assertions receive the same score, while parameter modularity allows for the independent treatment of parameters in different network structures. These properties simplify the encoding of user knowledge and enable the combination of prior knowledge with statistical data. The paper discusses the use of Bayesian principles to develop algorithms that take user knowledge (expressed as a prior Bayesian network) and statistical data as inputs, and return improved Bayesian networks. It describes the scoring metric for belief networks, which is similar to existing metrics but scores directed networks rather than undirected ones. The authors also introduce the concept of event equivalence, which is crucial for ensuring that isomorphic belief networks receive the same score. The paper introduces the BDe metric, a score-equivalent metric for belief networks that incorporates a prior belief network and an equivalent sample size. This metric allows for the combination of user knowledge and statistical data, and is shown to exhibit score equivalence. The BDe metric is evaluated on the Alarm network, demonstrating its effectiveness in learning Bayesian networks from data. The paper also discusses the limitations of the BDe metric, particularly in cases where the prior knowledge is not accurate or complete. It suggests that while score equivalence is important, other assumptions such as Dirichlet priors may be relaxed in certain situations. The authors conclude that the BDe metric provides a powerful tool for learning Bayesian networks from a combination of user knowledge and statistical data.