I'm curious how much professional statistical experience you have? In my experience probabilities alone are very rarely used and distributions of beliefs are co

I'm curious how much professional statistical experience you have? In my experience probabilities alone are very rarely used and distributions of beliefs are combined with distributions of value so you can choose optimal risk/reward scenarios. Bayesian decision making typically involves combining a cost function with your posterior distribution. It's worth pointing out that this is typically not possible in most frequentist frameworks since they work in double negative style assertions and arbitrary threshold rather than modeling the problem itself. While you can map Bayesian approaches to frequentists tests, this is usually a misunderstanding of Bayesian methods coming from a purely frequentist background. Bayesian analysis is fundamentally more flexible since it just the application of the sum and product rules (you don't even need Bayes' theorem since it can be trivially derived from these) as well as corresponding cost/value functions.