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Assessing evidence in multiple hypotheses
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AI
DOI：10.2307/2291745.png)
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摘要
En 中文
We formulate the problem of choosing between two hypotheses as a problem of constructing a data-dependent evidential measure for or against the null hypothesis. Our main focus is on the multivariate case, and in particular we examine multivariate evidential measures constructed as combinations of univariate ones. Such measures should obey some minimal intuitive desiderata, which we state as axioms. These axioms formalize the acceptable behavior for various values of the individual pieces of evidence, and we discuss in detail the rationale behind each axiom. Furthermore, we investigate other properties of multivariate evidence that are desirable but not indispensable. These properties consider mainly the performance of methods of combination of evidence as the dimension of the problem varies. We critically examine the behavior of common rules of assessing evidence in higher dimensions, such as combinations of p values and Bayes posterior probabilities, and clarify the connection between hypothesis testing and our approach. We include a discussion comparing different methods of assessing evidence.
Keyword:
Bayesian posterior probabilities
combining experiments
hypothesis testing
meta-analysis
p values
