Probability, belief and success rate: comments on ‘On the meaning of coverage probabilities’

Abstract

The method of uncertainty evaluation discussed in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement generates a coverage interval in which the measurand is said to have a certain probability (the coverage probability) of lying. This communication contains a response to the recent claim that 'when a coverage interval summarizes the resulting state of knowledge, the coverage probability should not be interpreted as a relative frequency of successful intervals in a large series of imagined or simulated intervals' (Lira 2009 Metrologia 46 616–8 ). First, Bernoulli's law of large numbers is used to prove that the long-run success rate of a methodology used to calculate 95% coverage intervals must be 95%. Second, the usual definition of subjective probability or 'degree of belief' is stated, and the weak law of large numbers is then used to show that this definition—and the corresponding definition of 'state of knowledge'—relies on the concept of long-run behaviour. This provides an alternative proof of the same result.

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