Incorporating Expert Opinion in an Inferential Model while Maintaining Validity

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Leonardo Cella, Ryan Martin ;
Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 103:68-77, 2019.

Abstract

The incorporation of partial prior information in statistical inference problems still lacks a definitive answer. The two most popular statistical schools of thought deal with partial priors in different ways: they either get completely ignored (frequentist approach) or they are transformed into a “complete” prior information, i.e., a probability distribution (Bayesian approach). Acknowledging the importance of (i) taking into account all sources of relevant information in a given problem and (ii) controlling error probabilities, the present paper provides insights on how to incorporate partial priors “as they are”. This incorporation is guided by desired properties, such as that correct partial priors should result in more efficient inferences and, most importantly, that the inferences are always calibrated, independent of the truthfulness of the partial prior.

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