Nested Hypothesis Testing: The Bayesian Reference Criterion

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Abstract
It is argued that hypothesis testing problems are best considered as decision problems concerning the choice of a usejul probability model. Decision theory, information measures and reference analysis, are combined to propose a non-subjective Bayesian approach to nested hypothesis testing, the Bayesian Reference Criterion (BRC). The results are compared both with frequentist based procedures, and with the use of Bayes factors. The theory is illustrated with stylized examples, where alternative approaches may easily be compared.

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