Unified Approach for Frequentist and Bayesian Testing

What is it about?

Modern theory for statistical hypothesis testing can broadly be classified as Bayesian or frequentist. Unfortunately, one can reach divergent conclusions if Bayesian and frequentist approaches are applied in parallel to analyze the same data set. This is a serious impasse since there is a lack of consensus on when to use one approach in detriment of the other. To resolve this historical lack, a unified approach is derived in this paper.

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Why is it important?

Fundamentals of frequentist and Bayesian approaches for hypothesis testing are revisited in order to state the analytical arguments for a reconciling theorem. This theorem is then proved for the general case of any hypothesis testing problem.

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