Consistency in Statistical Inference and Decision

TLDR

The concept introduces medial personal probabilities that follow classical probability laws but are defined only within intervals. The study proposes that belief strength can be assessed by the odds at which a person is willing to bet on those beliefs. Bayes’ Theorem is used for inference, and decisions are made by maximizing expected utility under general conditions. The approach yields widely accepted large‑sample statistical procedures, but emphasizes weight of evidence rather than significance level as the conviction metric in hypothesis testing.

Abstract

SUMMARY It is suggested that the strength of a person’s beliefs may be tested by finding at what odds he is prepared to bet on them. This leads to a system of numerical “medial personal probabilities” obeying the classical laws of probability. However, these do not have precisely defined values, but are contained within specified intervals. The appropriate method of inference is Bayes’s Theorem. This leads to generally accepted statistical procedures in large samples, except that the “weight of evidence” and not significance level is the measure of conviction in a significance test. Under very general conditions decisions are made by maximizing expected utility.