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Statistical ThoughtA Perspective and History$
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Shoutir Kishore Chatterjee

Print publication date: 2003

Print ISBN-13: 9780198525318

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525318.001.0001

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INTERPRETATION OF PROBABILITY: VARIOUS NUANCES

INTERPRETATION OF PROBABILITY: VARIOUS NUANCES

Chapter:
(p.36) 3 INTERPRETATION OF PROBABILITY: VARIOUS NUANCES
Source:
Statistical Thought
Author(s):

Shoutir Kishore Chatterjee

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525318.003.0003

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

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