Chapter

INTERPRETATION OF PROBABILITY: VARIOUS NUANCES

Shoutir Kishore Chatterjee

in Statistical Thought

Published in print May 2003 | ISBN: 9780198525318
Published online September 2007 | e-ISBN: 9780191711657 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198525318.003.0003
 INTERPRETATION OF PROBABILITY: VARIOUS NUANCES

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Apart from formal operations, the interpretation of probability must be considered to use probability for statistical induction. The objective interpretation relates probability to long-term relative frequency, but even here there are diverse viewpoints such as those of von-Mises-Reichenbach, Fisher-Russell, and Kolmogorov-Cramer-Neyman. Further, under this interpretation, different solutions have been proposed for the instantiation problem. Subjective interpretation, which attaches probability to uncertain propositions, has an impersonal version due to Keynes-Jeffreys and a personal one due to Ramsey-deFinnetti. Although the axiomatics are common for the standard interpretations, evaluations are different and principles like independence, coherence, and exchangeability have varying importance for different types of probability. For certain statistical applications, approximate evaluation of probability also assumes importance.

Keywords: objective interpretation; long-term relative frequency; instantiation; subjective interpretation; impersonal; personal; axiomatics; approximate probability

Chapter.  13476 words. 

Subjects: Probability and Statistics

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