It is my understanding that one can easily model prior knowledge about variables or even models with Bayesian statistics. In a certain way, Bayesian stats "forces you" to think about prior knowledge and modeling it explicitly with distributions. It is also my understanding that the only thing that is "fixed" (provided) in Bayesian statistics is "the actual estimator", whereas in frequentist statistics, there are many types of theoretically defined estimators, and much science goes to that.
- Is my understanding above correct?
- Are there any other frameworks that help a modeler define prior beliefs explicitly other than Bayesian statistics? Perhaps frameworks that don't require e.g. normalization such as energy-based models? Or is Bayesian statistics truly the only framework where reasoning over prior knowledge is well defined.