A Bayesian interpretation of possibility theory applied to the replication crisis & model checking

What is it about?

Under a simple class of utility functions, the Bayes-optimal estimates can be formulated using possibility theory instead of probability theory. This interpretation of possibility theory reduces to the likelihood interpretation for a special case of the utility function and the prior possibility measure.

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Why is it important?

Applications include not only a formalization of Bayesian model checking and updating but also a method of null hypothesis significance testing in the absence of a completely specified space of alternative hypotheses. That method addresses the replication crisis by weighing relative payoffs for not rejecting the null hypothesis when it holds and or rejecting it when a specified alternative hypothesis holds.

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