A Bayesian network, Bayes network, belief network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). (Wikipedia)
Global optimization of expensive, potentially gradient-free functions has long been a critical component of many complex problems in science and engineering.
Bayesian model evidence gives a clear criteria for such model selection. However, computing model evidence requires integration over the likelihood, which is challenging, particularly when the likelihood is non-closed-form and/or expensive.