An Essay on the Double Nature of the Probability

Paolo Rocchi, Leonida Gianfagna

IBM, via Shangai 53, Roma, Italy.

DOI: 10.4236/apm.2012.25041                

Abstract

Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that appear incompatible. This discrepancy raises ample debates and the foundations of the probability calculus emerge as a tricky, open issue so far. Instead of developing philosophical discussion, this research resorts to analytical and mathematical methods. We present two theorems that sustain the validity of both the frequentist and the subjective views on the probability. Secondly we show how the double facets of the probability turn out to be consistent within the present logical frame.

Keywords

Theory of Probability; Subjectivism; Frequentism; Theorem of Large Numbers; Probability Dualism

Conflicts of Interest

The authors declare no conflicts of interest.

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