Open Access: Objective priors in the empirical Bayes framework

Each week, we select a recently published Open Access article to feature. This week’s article comes from the Scandinavian Journal of Statistics and introduces a nonparametric, transformation-invariant estimator for the prior distribution. 

The article’s abstract is given below, with the full article available to read here.

Klebanov, ISikorski, ASchütte, CRöblitz, SObjective priors in the empirical Bayes frameworkScand J Statist2021481212– 1233

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.

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