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Abstract:
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Any decision process is associated with the possibility of committing errors. When two hypotheses are considered, frequentist methods introduced by R.A. Fisher and extended by Neyman-Pearson control the maximum probability decision error of the null hypothesis to be while minimizing the probability of the type II error. On the other hand, Bayesian methods minimize the linear combination of decision error probabilities of both hypotheses. However, these errors are typically unmeasured and uncontrolled. Scientists wish to control both errors when testing hypotheses. A known strategy is through sequential sampling, even though the possibility of continuous sampling until a decision can be reached is uncommon in practice. Usually, sample sizes are fixed. To control both decision errors something got to give: one needs to include a third possibility, that neither of the two hypotheses can be accepted. We remain undecided, or agnostic. We present a Bayesian agnostic test that controls the average predictive probability of decision errors that is also suitable for multiple hypothesis testing and, by controlling all the decision-error probabilities, favors reproducibility.
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