Classical approaches to statistical inference developed by Fisher and by Neyman & Pearson largely eschew Bayes' theorem and are therefore non-Bayesian.

Elements of a logicist conception of inductive logic live on today as part of the general approach called Bayesian inductive logic. However, among philosophers and statisticians the term ‘Bayesian’ is now most closely associated with the subjectivist or personalist account of belief and decision. And the term ‘Bayesian inductive logic’ has come to carry the connotation of a logic that involves purely subjective probabilities. This usage is misleading since, for inductive logics, the Bayesian/non