Cited by 1,448Statistical Methods and Bayesian InferenceStatistical Methods and InferenceStatistical Distribution Estimation and Applications

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Parametric Empirical Bayes Inference: Theory and Applications

Morris, Carl N.·1983·Journal of the American Statistical Association

DOI 10.1080/01621459.1983.10477920

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Abstract

This article reviews the state of multiparameter shrinkage estimators with emphasis on the empirical Bayes viewpoint, particularly in the case of parametric prior distributions. Some successful applications of major importance are considered. Recent results concerning estimates of error and confidence intervals are described and illustrated with data.

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Method
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“2013, 32 1691–1706 1701 For our data analysis, we just need to replace 2 and 2 by their estimators O 2 and O 2 in Qıi , i D 1, . . . s, and Qı to have OQı D Xs iD1 Oıi= O 2C 2 O 2=Ni = Xs iD1 1= O 2C 2 O 2=Ni and OQıi D Oıi C 2 O 2=Ni O 2C 2 O 2=Ni OQı Oıi ; i D 1; 2; : : :; s: (28) As the estimators of 2 and 2 are us…”
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BackgroundMethod
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Lai, H.-L., & Helser, T. E. (2004) · Fisheries Research · doi:10.1016/j.fishres.2004.08.014 · Cited by 44
EMPIRICAL BAYES ESTIMATORS OF SMALL AREA PROPORTIONS IN MULTISTAGE DESIGNS
Farrell, P. J., MacGibbon, B., & Tomberlin, T. J. (1997) · Cited by 44
Empirical Bayes and Item-Clustering Effects in a Latent Variable Hierarchical Model
Scott, S. L., & Ip, E. (2002) · Journal of the American Statistical Association · doi:10.1198/016214502760046961 · Cited by 49
“The subgroup comparisons that NAEP report are of great interest to the general public, because they are often cited to support speci c educational and political agendas.”
Background
Hierarchical Models for the Probabilities of a Survey Classification and Nonresponse: An Example from the National Crime Survey
Stasny, E. A. (1991) · Journal of the American Statistical Association · doi:10.1080/01621459.1991.10475033 · Cited by 44
“Saphire (1989) developed hierarchical models for estimating the number of victimizations experienced by an HH that make use of covariates but do not address the nonresponse problem.”
Background
Estimation in Bayesian Disease Mapping
MacNab, Y. C., Farrell, P. J., Gustafson, P., & Wen, S. (2004) · Biometrics · doi:10.1111/j.0006-341x.2004.00241.x · Cited by 44
“This phenomenon reveals a shortcoming in the EB interval defined in Morris (1983), where C(y) is defined as an EB confidence interval of size 1 − α for αj if PΘ[αj ∈ C(y)] ≈ 1 − α for all Θ. Note that the definition is an unconditional property.”
Background
Estimation of an overall standardized mean difference in random‐effects meta‐analysis if the distribution of random effects departs from normal
Rubio‐Aparicio, M., López-López, J. A., Sánchez‐Meca, J., Marín‐Martínez, F., Viechtbauer, W., & Noortgate, W. V. D. (2018) · Research Synthesis Methods · doi:10.1002/jrsm.1312 · Cited by 43
Prevalence, impact and treatment of generalised anxiety disorder in bipolar disorder: a systematic review and meta-analysis
Preti, A., Vrubļevska, J., Veroniki, A. A., Huedo-Medina, T. B., & Fountoulakis, K. Ν. (2016) · Evidence-Based Mental Health · doi:10.1136/eb-2016-102412 · Cited by 45
Combining Expert Judgment by Hierarchical Modeling: An Application to Physician Staffing
Lipscomb, J., Parmigiani, G., & Hasselblad, V. (1998) · Management Science · doi:10.1287/mnsc.44.2.149 · Cited by 43
Some Bayesian and Non-Bayesian Procedures for the Analysis of Comparative Experiments and for Small-Area Estimation: Computational Aspects, Frequentist Properties, and Relationships
Hulting, F. L., & Harville, D. A. (1991) · Journal of the American Statistical Association · doi:10.1080/01621459.1991.10475080 · Cited by 47
“where and the population means of aj' and fc' for the small-area and where = Fj Following Prasad and Rao (1986) and Battese and Fuller (1981), we assume that the population size for the area is large, in which case % 0 (i.”
Background
Robust Empirical Bayes Confidence Intervals
Armstrong, T. B., Kolesár, M., & Plagborg‐Møller, M. (2022) · Econometrica · doi:10.3982/ecta18597 · Cited by 48
“The natural EB version of a confidence interval (CI) takes the form of a Bayesian credible interval, again using the postulated effect distribution as a prior (Morris (1983b)).”
BackgroundMethodInfluential
On Inadmissibility of Some Unbiased Estimates of Loss
Johnstone, I. M. (1988) · Springer eBooks · doi:10.1007/978-1-4613-8768-8_33 · Cited by 42
Partially pooled covariance matrix estimation in discriminant analysis
Greene, T., & Rayens, W. S. (1989) · Communication in Statistics- Theory and Methods · doi:10.1080/03610928908830117 · Cited by 42
A Bayesian strategy for screening cancer treatments prior to phase II clinical evaluation.
Thall, P., & Estey, E. (1993) · Statistics in Medicine · doi:10.1002/sim.4780121303 · Cited by 42
Teachers and Urban‐Rural Gaps in Educational Outcomes
Zhang, J., Jin, S., Torero, M., & Li, T. (2018) · American Journal of Agricultural Economics · doi:10.1093/ajae/aay009 · Cited by 44
“Having obtained estimates ĉ and ŝ of the model parameters c and s, we predict values of the random teacher effect lj for each teacher j through the empirical Bayes prediction method (Morris 1983; Raudenbush and Bryk 2002; Rabe-Hesketh and Skrondal 2008).”
Method
Shrinkage of Value-Added Estimates and Characteristics of Students with Hard-to-Predict Achievement Levels
Herrmann, M., Walsh, E., & Isenberg, E. (2016) · Statistics and Public Policy · doi:10.1080/2330443x.2016.1182878 · Cited by 41
“To see this, consider the EB shrinkage procedure outlined in Morris (1983).”
Method
Modelling the female‐to‐male per‐act HIV transmission probability in an emerging epidemic in Asia
Satten, G. A., Mastro, T. D., & Longini, I. M. (1994) · Statistics in Medicine · doi:10.1002/sim.4780131918 · Cited by 41
Statistical Modelling of Citation Exchange Between Statistics Journals
Varin, C., Cattelan, M., & Firth, D. (2015) · Journal of the Royal Statistical Society Series A (Statistics in Society) · doi:10.1111/rssa.12124 · Cited by 40
“Shrinkage estimation offers notable improvement over standard maximum likelihood estimation when the target is simultaneous estimation of a vector of mean parameters; see, for example, Morris (1983).”
Background
Comorbidity of obsessive-compulsive disorder in bipolar spectrum disorders: Systematic review and meta-analysis of its prevalence
Ferentinos, P. P., Preti, A., Veroniki, A. A., Pitsalidis, K. G., Antonis, T., Antoniou, A., & Fountoulakis, K. Ν. (2019) · Journal of Affective Disorders · doi:10.1016/j.jad.2019.11.136 · Cited by 41
General empirical Bayes wavelet methods and exactly adaptive minimax estimation
Zhang, C.-H. (2005) · The Annals of Statistics · doi:10.1214/009053604000000995 · Cited by 40
“We further refer to Morris (1983), Robbins (1983) and Berger (1985) for general discussion about EB and Bayes methods.”
Background
The Returns to College(s): Relative Value-Added and Match Effects in Higher Education
Mountjoy, J., & Hickman, B. (2020) · doi:10.2139/ssrn.3537773 · Cited by 41
An Empirical Bayes Procedure for Improving Individual-Level Estimates and Predictions From Finite Mixtures of Multinomial Logit Models
Kamakura, W. A., & Wedel, M. (2004) · Journal of Business and Economic Statistics · doi:10.1198/073500103288619449 · Cited by 39
“yijXi; O μt/ : (5) These posterior probabilities and individual-level estimates are thus computed in the tradition of the parametric empirical Bayes approaches (Deely and Lindley 1981; Morris 1983), by plugging the MLEs of the hyperparameters, O 2, into the expressions for the individual-levelestimates and predictions…”
Method

Authors: Morris, C. N.
Affiliations: The University of Texas at Austin (US)
Corresponding author: Morris, Carl N.
Venue: Journal of the American Statistical Association
Publisher: Informa UK Limited
Published: 1983-03
Volume: 78
Issue: 381
Pages: 47-55
ISSN: 0162-1459 (ISSN-L)
1537-274X
DOI: 10.1080/01621459.1983.10477920
OpenAlex: W1983607152
Cited by: 1,448
References: 36
Citations by year: 2026: 32 · 2025: 30 · 2024: 52 · 2023: 42 · 2022: 40 · 2021: 51 · 2020: 62 · 2019: 44 · 2018: 49 · 2017: 43 · 2016: 54 · 2015: 63 · 2014: 66 · 2013: 49 · 2012: 48
FWCI: 24.44
Type: journal article
Language: en
Open access: closed
Locations: Journal of the American Statistical Association (publishedVersion)
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords: parametric empirical Bayes, confidence intervals, shrinkage estimation

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Parametric Empirical Bayes Inference: Theory and Applications

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