The classical or frequentist approach to statistics (in which inference is centered on significance testing), is associated with a philosophy in which science is deductive and follows Popperis doctrine of falsification. In contrast, Bayesian inference is commonly associated with inductive...

An elementary sketch of some issues in statistical inference and in particular of the central role of likelihood is given. This is followed by brief outlines of what George Barnard considered were the four great systems of statistical inferences. These can be thought of terms of the four...

Inability to clearly defend against the criticisms of frequentist methods has turned many a frequentist away from venturing into foundational battlegrounds. Conceding the distorted perspectives drawn from overly literal and radical expositions of what Fisher, Neyman, and Pearson ‘really...