THE MEANING OF PROBABILITY FROM A FOUNDATIONAL PERSPECTIVE

Abstract

We focus on the ways in which we can use a frequentist interpretation of probability to develop suitable methods for statistical inference. The discussion about the controversy in the foundations reveals that a frequentist conception is highly prone to dispute, as a justification of it fails from a rational perspective when the explication of probability integrates statistical inference. We give an overview on the dispute and the crucial examples that highlight the deficiencies of a purely frequentist position towards probability. The concept of probability emerges from a mixture of meanings. A shift in connotation of probability towards a biased frequentist meaning decreases the scope of probability or the quality of applications. Probability is a complementary concept, which falls apart if we reduce it to one view. This gives rise to investigate approaches towards teaching from a wider perspective on the range of meanings of probability apart from frequentist aspects. Empirical studies show the shortcomings of educational approaches that ignore subjectivist aspects of probability, which leads to far-reaching misconceptions not only about the use of Bayes’ formula but also in the perception of probabilities at large.