Confirming power of observations metricized for decisions among hypotheses

Philosophy of Science 27 (3):293-307 (1960)
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Abstract

Experimental observations are often taken in order to assist in making a choice between relevant hypotheses ∼ H and H. The power of observations in this decision is here metrically defined by information-theoretic concepts and Bayes' theorem. The exact (or maximum power) of a new observation to increase or decrease Pr(H) the prior probability that H is true; the power of that observation to modify the total amount of uncertainty involved in the choice between ∼ H and H: the power of a new observation to reduce uncertainty toward the ideal amount, zero; all these powers are systematically shown to be exact metrical functions of Pr(H) and Pr(o/H)/Pr(o)-1 where the numerator is the likelihood of the new observation given H, and the denominator is the "expectedness" of the observation

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