The foundations of probability deal with the problem of modelling reasoning in face of uncertainty by a mathematical calculus, usually the standard probability calculus (although there are alternatives in the literature).

The three dominating schools in the foundations of probability interpret probabilities as

Apart from the interpretation of probability, frequentism and Bayesianism in particular also differ with respect to the advocated methodology for inference. Frequentists use tests, estimators, and confidence intervals (although the frequentist interpretation of probability itself does not preclude the use of other techniques including Bayesian ones if they have good frequentist properties in the given situation). Bayesians usually start with a prior distribution and use the posterior distribution, which is obtained by conditioning on the evidence, in order to carry out inferences. The prior distribution either models the individual’s personal...