Empirical Bayes methods in high dimensions: a survey and ongoing debates

Stefano Rizzelli ()
Additional contact information
Stefano Rizzelli: University of Padova, Department of Statistics

METRON, 2025, vol. 83, issue 3, No 2, 313-331

Abstract: Abstract Bayesian inference has as its starting point the specification of a prior distribution on the (possibly infinite-dimensional) parameters of the adopted statistical model. In some cases, a specification genuinely based on information available a priori and formalizing one’s level of uncertainty is difficult. This is especially true for the high-dimensional models in use for complex, recent applications of statistics and machine learning. In such circumstances, a popular practice, known as empirical Bayes, is to fix the value of the most relevant prior hyperparameters through the data. Notable examples are hyperparameters controlling sparsity in linear regression or sequence models; complexity in model selection or neural networks architecture; smoothness in nonparametric regression or density estimation. In spite of their popularity, empirical Bayesian methods still raise concerns of degeneracies and poor uncertainty quantification on the part of some scholars and practitioners, especially when set against fully Bayesian methods, whereby a hyperprior is specified on hyperparameters. The aim of this paper is to bring clarity by providing a critical review of recent advances in empirical Bayes methods for high-dimensional analysis. We offer an overview of their theoretical properties using the notion of oracle priors, illustrating with examples different facets of posterior adaptation. Finally, we discuss open issues, actively researched topics and future prospects.

Keywords: Marginal likelihood; Adaptive posterior distributions; High-dimensional analysis; Gaussian process; Sparse sequence model (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s40300-025-00293-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metron:v:83:y:2025:i:3:d:10.1007_s40300-025-00293-y

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/40300

DOI: 10.1007/s40300-025-00293-y

Access Statistics for this article

METRON is currently edited by Marco Alfo'

More articles in METRON from Springer, Sapienza Università di Roma
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().