Incorporating Expert Opinion in an Inferential Model while Maintaining Validity

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v103-cella19a, title = {Incorporating Expert Opinion in an Inferential Model while Maintaining Validity}, author = {Cella, Leonardo and Martin, Ryan}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {68--77}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/cella19a/cella19a.pdf}, url = {https://proceedings.mlr.press/v103/cella19a.html}, 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.} }
Endnote
%0 Conference Paper %T Incorporating Expert Opinion in an Inferential Model while Maintaining Validity %A Leonardo Cella %A Ryan Martin %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-cella19a %I PMLR %P 68--77 %U https://proceedings.mlr.press/v103/cella19a.html %V 103 %X 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.
APA
Cella, L. & Martin, R.. (2019). Incorporating Expert Opinion in an Inferential Model while Maintaining Validity. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:68-77 Available from https://proceedings.mlr.press/v103/cella19a.html.

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