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Objective priors in the empirical Bayes framework
Author(s) -
Klebanov Ilja,
Sikorski Alexander,
Schütte Christof,
Röblitz Susanna
Publication year - 2021
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12485
Subject(s) - prior probability , overfitting , mathematics , bayes' theorem , econometrics , estimator , nonparametric statistics , bayesian probability , inference , artificial intelligence , statistics , computer science , artificial neural network
When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data‐driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation‐invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data‐driven setting. This implies a natural interpretation as a trade‐off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies.