INTERPRETATION OF PROBABILITY: VARIOUS NUANCES
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.
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