Frequentism✩
Pub. online: 19 December 2022
Type: Statistical Methodology
Open Access
Open Access
✩
Main article: https://doi.org/10.51387/22-NEJSDS4.
Accepted
16 August 2022
16 August 2022
Published
19 December 2022
19 December 2022
Abstract
Discussion of “Four types of frequentism and their interplay with Bayesianism” by Jim Berger.
References
Abraham, K., Castillo, I. and Roquain, E. (2022). Empirical Bayes cumulative ℓ-value multiple testing procedure for sparse sequences. Electron. J. Stat. 16(1) 2033–2081. https://doi.org/10.1214/22-ejs1979. MR4415394
Berger, J. O. (1985) Statistical decision theory and Bayesian analysis second ed. Springer Series in Statistics. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4757-4286-2. MR804611. https://doi-org.tudelft.idm.oclc.org/10.1007/978-1-4757-4286-2.
Castillo, I. and Roquain, E. (2020). On spike and slab empirical Bayes multiple testing. Ann. Statist. 48(5) 2548–2574. https://doi.org/10.1214/19-AOS1897. MR4152112.
Efron, B. (2010) Large-scale inference. Institute of Mathematical Statistics (IMS) Monographs 1. Cambridge University Press, Cambridge. Empirical Bayes methods for estimation, testing, and prediction. https://doi.org/10.1017/CBO9780511761362. MR2724758. https://doi-org.tudelft.idm.oclc.org/10.1017/CBO9780511761362.
Jiang, W. and Zhang, C. -H. (2009). General maximum likelihood empirical Bayes estimation of normal means. Ann. Statist. 37(4) 1647–1684. https://doi.org/10.1214/08-AOS638. MR2533467.
Knapik, B. T., van der Vaart, A. W. and van Zanten, J. H. (2011). Bayesian inverse problems with Gaussian priors. Ann. Statist. 39(5) 2626–2657. https://doi.org/10.1214/11-AOS920. MR2906881.
Le Cam, L. (1986) Asymptotic methods in statistical decision theory. Springer Series in Statistics. Springer-Verlag, New York. https://doi.org/10.1007/978-1-4612-4946-7. MR856411. https://doi-org.tudelft.idm.oclc.org/10.1007/978-1-4612-4946-7.
Robbins, H. (1964). The empirical Bayes approach to statistical decision problems. Ann. Math. Statist. 35 1–20. https://doi.org/10.1214/aoms/1177703729. MR163407.
Sniekers, S. and van der Vaart, A. (2020). Adaptive Bayesian credible bands in regression with a Gaussian process prior. Sankhya A 82(2) 386–425. https://doi.org/10.1007/s13171-019-00185-0. MR4136240.
Szabó, B., van der Vaart, A. and van Zanten, H. (2015). Honest Bayesian confidence sets for the ${L^{2}}$-norm. J. Statist. Plann. Inference 166 36–51. https://doi.org/10.1016/j.jspi.2014.06.005. MR3390132.
Taylor, J. E. (2018). A selective survey of selective inference. In Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. IV. Invited lectures 3019–3038. World Sci. Publ., Hackensack, NJ. MR3966521.
van der Pas, S., Szabó, B. and van der Vaart, A. (2017). Uncertainty quantification for the horseshoe (with discussion). Bayesian Anal. 12(4) 1221–1274. With a rejoinder by the authors. https://doi.org/10.1214/17-BA1065. MR3724985.
van der Vaart, A. (2002). The statistical work of Lucien Le Cam. Ann. Statist. 30 631–682. Dedicated to the memory of Lucien Le Cam. https://doi.org/10.1214/aos/1028674836. MR1922537. https://doi-org.tudelft.idm.oclc.org/10.1214/aos/1028674836.
