On the Empirical Adequacy of Composite Statistical Hypotheses

Abstract
According to van Fraassen's constructive empiricism, the epistemological aim of scientific theories is "to save the phenomena". Theories which achieve this aim are said to be empirically adequate. In an earlier paper a likelihood analysis of the empirical adequacy of simple statistical hypotheses was given. The present paper extends that likelihood analysis of empirical adequacy to composite statistical hypotheses. It is argued that for composite hypotheses the notion of likelihood is ambiguous. This ambiguity leads to a distinction between predictive adequacy, based upon a prior likelihood function, and descriptive adequacy, based upon a posterior likelihood function.
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