“Lindley’s Paradox”, 1982 ():
A sharp null hypothesis may be strongly rejected by a sampling-theory test of statistical-significance and yet be awarded high odds by a Bayesian analysis based on a small prior probability for the null hypothesis and a diffuse distribution of one’s remaining probability over the alternative hypothesis.
The Bayesian analysis seems to interpret the diffuse prior as a representation of strong prior evidence, and this may be questionable.
The theory of belief functions allows us to represent the strength of prior evidence more realistically.
These ideas are illustrated by the problem of identifying glass by its refractive index.
[Keywords: Bayesian inference; belief functions: conflicting evidence, Dempster’s rule, discounting, statistical-significance testing]
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