Empirical Bayes
Empirical Bayes (EB) is an estimation strategy, introduced by Herbert Robbins in 1956 and developed into practical shrinkage estimators by Bradley Efron and Carl Morris in 1973, in which the hyperparameters of the prior distribution are estimated from the observed data via the marginal likelihood rather than specified in advance. The resulting posterior retains a Bayesian structure but substitutes data-driven hyperparameters for subjective ones, bridging frequentist shrinkage and full Bayesian inference.
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- Robbins, H. (1956). An empirical Bayes approach to statistics. In J. Neyman (Ed.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1 (pp. 157–164). University of California Press. · DOI 10.1525/9780520313880-015
- Efron, B., & Morris, C. (1973). Stein's estimation rule and its competitors — An empirical Bayes approach. Journal of the American Statistical Association, 68(341), 117–130. · DOI 10.1080/01621459.1973.10481350
- Carlin, B. P., & Louis, T. A. (2000). Bayes and Empirical Bayes Methods for Data Analysis (2nd ed.). Chapman & Hall/CRC. · ISBN 978-1584881704
- Efron, B., & Hastie, T. (2016). Computer Age Statistical Inference: Algorithms, Evidence, and Data Science. Cambridge University Press. · ISBN 978-1107149892
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