Mutual Influence between Different Views of Probability and Statistical Inference

Palabras clave: Intuitive views, Foundations of probability, Bayesian controversy, Justification of probability, Bayes theorem, Statistical tests


In this paper, we analyse the various meanings of probability and its different applications, and we focus especially on the classical, the frequentist, and the subjectivist view. We describe the different problems of how probability can be measured in each of the approaches, and how each of them can be well justified by a mathematical theory. We analyse the foundations of probability, where the scientific analysis of the theory that allows for a frequentist interpretation leads to unsolvable problems. Kolmogorov’s axiomatic theory does not suffice to establish statistical inference without further definitions and principles. Finally, we show how statistical inference essentially determines the meaning of probability and a shift emerges from purely objectivist views to a complementary conception of probability with frequentist and subjectivist constituents. For didactical purpose, the result of the present analyses explains basic problems of teaching, originating from a biased focus on frequentist aspects of probability. It also indicates a high priority for the design of suitable learning paths to a complementary conception of probability. In the applications, modellers use information in a pragmatic way processing this information regardless of its connotation into formal mathematical models, which are always thought as essentially wrong but useful.


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Biografía del autor/a

Manfred Borovcnik, University of Klagenfurt
Professor at the Department of Statistics, University of Klagenfurt. Master in Mathematics, Doctor in Statistics. Member of the Ethics Commission of the Federal State of Carinthia. Elected member of the International Statistical Institute. Past vice president of the International Association for Statistics Education. Co-editor of Stochastik in der Schule  and  Co-editor of Statistics Education Research Journal. Research interest: Statistics and probability education  E-mail:


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Borovcnik, M. (2021). Mutual Influence between Different Views of Probability and Statistical Inference. PARADIGMA, 41(e1), 221-256.