The concept of probability, crisis in statistics, and the unbearable lightness of Bayesing

TL;DR

This paper discusses the crisis in statistical education and research, emphasizing the need to clarify the concept of probability by integrating Kolmogorov's objective models with Bayesian subjective approaches for better scientific understanding.

Contribution

It clarifies the concept of probability by distinguishing between Kolmogorov's objective models and Bayesian subjective probability, proposing a combined approach for scientific analysis.

Findings

Kolmogorov's probability models are scientifically grounded.

Bayesian probability is subjective and heuristic.

A combined approach enhances scientific conclusions.

Abstract

Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of probability. This article aims to separate the concept of probability which is scientifically based from other concepts that do not have this characteristic. The scientifically based concept of probability is Kolmogorovs concept of probability models together with the conditions of their applicability. Bayesian statistics is based on the subjective concept of probability, and as such can only have a heuristic value in searching for the truth, but it cannot and must not replace the truth. The way out of the crisis should take Kolmogorov and Bayesian analysis as elements, each of which has a well-defined and limited use. Only together with qualitative analysis and other types of quantitative analysis, and combined with experiments, they can contribute to reaching correct conclusions.