Picking Bayesian or Classical Statistics by Means of Mathematical Criteria

Classical and Bayesian statistics have own proper criteria and techniques. The scientific community debates the pros and cons of the two statistical schools since long, but this broad research driven by theoretical and practical criteria, has not provided definitive answers since a fundamental disagreement lies at the very heart of the problems. Conflicting probability theories underpin the two statistics and the numbers convey irreconcilable meanings in the two sectors. Eminent authors have developed philosophical arguments to support their probability interpretations, by contrast we have conducted an inquiry which follows a purely mathematical approach. Two theorems prove that the frequentist and subjective models are not incompatible and lead to a precise rule for working statisticians who are called to select the most suitable methods in a project.