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

The DOI matches its Crossref record; 34 of the 36 references it cites were found in a registry or an index.

Parametric Empirical Bayes Inference: Theory and Applications

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

DOI 10.1080/01621459.1983.10477920

Open this paper in CoChat — free account

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.

Integrity signals

Registry

Crossref · 10.1080/01621459.1983.10477920

Cites

34 of 34 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Cross validatory choice and assessment of statistical predictions
Stone, M. (1974) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1974.tb00994.x · Cited by 10,881
Journal of the Royal Statistical Society.
(1923) · The Economic Journal · doi:10.1093/ej/33.130.269 · Cited by 3,289
The Predictive Sample Reuse Method with Applications
Geisser, S. (1975) · Journal of the American Statistical Association · doi:10.1080/01621459.1975.10479865 · Cited by 2,748
Estimation with Quadratic Loss
James, W., & Stein, C. M. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-0919-5_30 · Cited by 2,319
Bayes Estimates for the Linear Model
Lindley, D. V., & Smith, A. F. M. (1972) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1972.tb00885.x · Cited by 2,025
Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data
Fay, R. E., & Herriot, R. A. (1979) · Journal of the American Statistical Association · doi:10.1080/01621459.1979.10482505 · Cited by 1,283
Stein's Estimation Rule and its Competitors—An Empirical Bayes Approach
Efron, B., & Morris, C. (1973) · Journal of the American Statistical Association · doi:10.1080/01621459.1973.10481350 · Cited by 981
Sampling and Bayes' Inference in Scientific Modelling and Robustness
Box, G. E. P. (1980) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2982063 · Cited by 905
Data Analysis Using Stein's Estimator and its Generalizations
Efron, B., & Morris, C. N. (1975) · Journal of the American Statistical Association · doi:10.1080/01621459.1975.10479864 · Cited by 863
An Empirical Bayes Approach to Statistics
Robbins, H. E. (1992) · Springer series in statistics · doi:10.1007/978-1-4612-0919-5_26 · Cited by 858

Show all 36 references

Research works printed but not linked: 8

Berger J., 1983, Robustness in Bayesian Statistics
Efron B., 1975, Advances in Mathematics, 16, 259
Gini C., 1911, Metron, 15, 133
Jackson D. A., 1970, Biometrika, 57, 439
Morris C., 1983, The Annals of Statistics, 11
Morris, C. and Van Slyke, L. “Empirical Bayes Methods for Pricing Insurance Classes,”. Proceedings of the Business and Economics Statistics Section. pp.579–582. American Statistical Association.
van der Merwe A. J., 1981, “Confidence Intervals for a Multivariate Normal Mean in the Case of Empirical Bayes Estimation Using Pearson Curves and Normal Approximations,”
Whitney, A. W. “The Theory of Experience Rating,”. Proceedings of the Casualty Actuarial Society. Vol. IV, pp.274–292.

Sorted by citations

Items 601–700 of 1,001

How do Test Scores at the Ceiling Affect Value-Added Estimates?
Resch, A., & Isenberg, E. (2018) · Statistics and Public Policy · doi:10.1080/2330443x.2018.1460226 · Cited by 18
“…preparation of value-added estimates, is used to handle imprecise estimates that arise from teachers who have a small number of students with valid test score data or many disadvantaged students whose post-test scores are relatively hard to predict (Morris 1983; Herrmann, Walsh, and Isenberg 2016).”
Background
The empirical Bayes estimators of the mean and variance parameters of the normal distribution with a conjugate normal-inverse-gamma prior by the moment method and the MLE method
Zhang, Y., Rong, T., & Li, M. (2019) · Communication in Statistics- Theory and Methods · doi:10.1080/03610926.2018.1465081 · Cited by 18
“Morris (1983) investigates the theory and applications of the parametric empirical Bayes inference.”
Data-driven Prognosis of Fatigue-induced Delamination in Composites using Optical and Acoustic NDE methods
Banerjee, P., Palanisamy, R. P., Haq, M., Удпа, Л., & Deng, Y. (2019) · IEEE Conference on Prognostics and Health Management · doi:10.1109/icphm.2019.8819426 · Cited by 18
“Contrary to regression, another popular approach for estimating unknown model parameter θ is via Bayes inference [34] which involves dynamic updation of the parameters such that the iterative prognosis algorithm is able to learn the underlying damage growth trend.”
Method
Implementation of quality controls is essential to prevent batch effects in breathomics data and allow for cross-study comparisons
Stavropoulos, G., Jonkers, D. M. A. E., Mujagic, Z., Koek, G. H., Masclee, A., Pierik, M. J., Dallinga, J. W., van Schooten, F., & Smolinska, A. (2020) · Journal of Breath Research · doi:10.1088/1752-7163/ab7b8d · Cited by 18
Posterior Average Effects
Bonhomme, S., & Weidner, M. (2021) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2021.1984928 · Cited by 18
“Posterior averaging is appealing for prediction purposes, and it plays a central role in Bayesian and empirical Bayes (EB) approaches (e.g., Berger 1980; Morris 1983).”
Background
Intelligent Smoothing Using Hierarchical Bayesian Models
Graham, P. J. (2008) · Epidemiology · doi:10.1097/ede.0b013e31816b7859 · Cited by 18
Sensitivity Analysis for Hierarchical Models Employing t Level-1 Assumptions
SELTZER, M. H., Novak, J. R., Choi, K., & Lim, N. (2002) · Journal of Educational and Behavioral Statistics · doi:10.3102/10769986027002181 · Cited by 18
An Empirical Bayes Group-Testing Approach to Estimating Small Proportions
Tebbs, J. M., Bilder, C. R., & Moser, B. K. (2003) · Communication in Statistics- Theory and Methods · doi:10.1081/sta-120019957 · Cited by 18
“For a thorough presentation of empirical Bayes (EB) and parametric EB theory, the reader is referred to Robbins (1964) and Morris (1983), respectively.”
Method
The risk of catastrophic failure of the solid rocket boosters on the space shuttle
Martz, H., & Zimmer, W. (1992) · The American Statistician · doi:10.1080/00031305.1992.10475846 · Cited by 18
The Notion of “Composite Reliability” and its Hierarchical Bayes Estimation
Chen, J., & Singpurwalla, N. D. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476715 · Cited by 18
Adjustment for smoking, alcohol consumption, and socioeconomic status in the california occupational mortality study
Beaumont, J. J., Singleton, J. A., Doebbert, G., Riedmiller, K. R., Brackbill, R. M., & Kizer, K. W. (1992) · American Journal of Industrial Medicine · doi:10.1002/ajim.4700210405 · Cited by 18
Estimating Physician Costliness
Miller, M. E., Hui, S. L., Tierney, W. M., & McDonald, C. J. (1993) · Medical Care · doi:10.1097/00005650-199305001-00004 · Cited by 18
A Discrimination Report Card
Kline, P., Rose, E. K., & Walters, C. (2024) · American Economic Review · doi:10.1257/aer.20230700 · Cited by 23
ACCOUNTING FOR BETWEEN‐STUDY VARIATION IN INCREMENTAL NET BENEFIT IN VALUE OF INFORMATION METHODOLOGY
Willan, A. R., & Eckermann, S. D. (2011) · Health Economics · doi:10.1002/hec.1781 · Cited by 17
An exponential partial prior for improving nonparametric maximum likelihood estimation in mixture models
Wang, J., & Lindsay, B. G. (2007) · Statistical Methodology · doi:10.1016/j.stamet.2007.03.004 · Cited by 17
“Here we propose an empirical Bayes (eB) approach due to [25,18], by which the hyperparameter ψ is estimated by maximum likelihood method based on the likelihood (4).”
Method
A New Method for Estimating Small Area Demographics and Its Application to Long-Term Population Projection
Inoue, T. (2016) · Applied demography series · doi:10.1007/978-3-319-43329-5_22 · Cited by 17
Post-audits for managing cyber security investments: Bayesian post-audit using Markov Chain Monte Carlo (MCMC) simulation
Herath, H. S. B., & Herath, T. C. (2018) · Journal of Accounting and Public Policy · doi:10.1016/j.jaccpubpol.2018.10.005 · Cited by 17
Implications of uniformly distributed, empirically informed priors for phylogeographical model selection: A reply to Hickerson et al.
Oaks, J. R., Linkem, C. W., & Sukumaran, J. (2014) · Evolution · doi:10.1111/evo.12523 · Cited by 17
“Thus, empirical Bayes methods have an uncertain theoretical basis and do not yield a valid posterior distribution from Bayes’ rule (e.g., empirical Bayesian estimates of the posterior are often too narrow, off-center, and incorrectly shaped; Morris, 1983; Laird and Louis, 1987; Carlin and Gelfand, 1990; Efron, 2013).”
BackgroundMethodInfluential
Comparison of Partially Measured Latent Traits across Nominal Subgroups
Cohen, J., & Jiang, T. (1999) · Journal of the American Statistical Association · doi:10.1080/01621459.1999.10473856 · Cited by 20
Hierarchical Bayes estimation of hunting success rates
He, Z., & Sun, D. (1998) · Environmental and Ecological Statistics · doi:10.1023/a:1009669302755 · Cited by 17
“Morris (1983) gives an excellent account of the empirical Bayes approach and significant applications.”
Background
Guided model checking with a Bayesian meta-heuristic
Seppi, K. D., Jones, M. D., & Lamborn, P. (2006) · Cited by 17
On Some Bayesian Solutions of the Neyman-Scott Problem
Ghosh, M. (1994) · Springer eBooks · doi:10.1007/978-1-4612-2618-5_20 · Cited by 17
On assessing the precision of Stein's estimator
Wen, X., & Judge, G. G. (1985) · Economics Letters · doi:10.1016/0165-1765(85)90169-7 · Cited by 17
Analysis of Agricultural Field Trials in the Presence of Outliers and Fertility Jumps
Taplin, R., & Raftery, A. E. (1991) · doi:10.21236/ada242454 · Cited by 17
Ability, Learning and the Career Path of Cardiac Specialists
Johnson, E. M. (2011) · Cited by 18
Application of the Bayesian approach for derivation of PDFs for concentration ratio values
Hosseini, A., Stenberg, K., Avila, R., Beresford, N. A., & Brown, J. E. (2013) · Journal of Environmental Radioactivity · doi:10.1016/j.jenvrad.2013.04.007 · Cited by 16
On SURE-Type Double Shrinkage Estimation
Jing, B., Li, Z., Pan, G., & Zhou, W. (2015) · Journal of the American Statistical Association · doi:10.1080/01621459.2015.1110032 · Cited by 16
The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function
Zhang, Y., Wang, Z., Duan, Z., & Mi, W. (2019) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2019.1652606 · Cited by 16
A Probabilistic Graphical Model-based Approach for Minimizing Energy Under Performance Constraints
Mishra, N., Zhang, H., Lafferty, J., & Hoffmann, H. (2015) · ACM SIGPLAN Notices · doi:10.1145/2775054.2694373 · Cited by 16
New large-sample confidence intervals for a linear combination of binomial proportions
Tebbs, J. M., & Roths, S. A. (2007) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2007.07.008 · Cited by 16
An empirical Bayes testing procedure for detecting variants in analysis of next generation sequencing data
Zhao, Z., Wang, W., & Wei, Z. (2013) · The Annals of Applied Statistics · doi:10.1214/13-aoas660 · Cited by 14
Small Area Estimation: A Review of Methods Based on theApplication of Mixed Models
Saei, A., & Chambers, R. L. (2003) · Cited by 16
Estimation in multi-arm two-stage trials with treatment selection and time-to-event endpoint
Brückner, M., Titman, A., & Jaki, T. (2017) · Statistics in Medicine · doi:10.1002/sim.7367 · Cited by 16
“In the normal case with known and equal variances and four or more treatment groups, the shrinkage estimator can be derived as an empirical Bayes estimator [24].”
MethodInfluential
On improving standard estimators via linear empirical Bayes methods
Samaniego, F. J., & Vestrup, E. (1999) · Statistics & Probability Letters · doi:10.1016/s0167-7152(99)00022-x · Cited by 16
Empirical Bayes methods for telecommunications forecasting
Greis, N. P., & Gilstein, C. Z. (1991) · International Journal of Forecasting · doi:10.1016/0169-2070(91)90053-x · Cited by 16
Forecasting from fallible data: Correcting prediction bias with stein‐rule least squares
Stanley, T. D. (1988) · Journal of Forecasting · doi:10.1002/for.3980070203 · Cited by 16
Confidence intervals for post‐test probability
Monsour, M., Evans, A. T., & Kupper, L. L. (1991) · Statistics in Medicine · doi:10.1002/sim.4780100316 · Cited by 16
Bayesian Estimation in the Presence of Deterministic Nuisance Parameters—Part II: Estimation Methods
Bar, S., & Tabrikian, J. (2015) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2015.2468680 · Cited by 15
“The first is inspired with the approach of parametric empirical Bayes [12], [13].”
Method
Uniform rates of the Glivenko–Cantelli convergence and their use in approximating Bayesian inferences
Dolera, E., & Regazzini, E. (2019) · Bernoulli · doi:10.3150/18-bej1077 · Cited by 15
“These difficulties are very often circumvented by the use of unorthodox, but more manageable, Bayesian methods, such as: empirical Bayes (see [30, 45, 47, 51]); partial and profile likelihood (see [21, 54]); numerical techniques based on simulation of random quantities, like the bootstrap (see [29, 30]).”
Method
Estimating variance of random effects to solve multiple problems simultaneously
Hirose, M. Y., & Lahiri, P. (2018) · The Annals of Statistics · doi:10.1214/17-aos1600 · Cited by 15
“Morris (1983) discussed an empirical Bayesian estimation of θi for a Bayesian model that is equivalent to the balanced case of NHM, that is, when Di = D implying Bi = B, i = 1, . . . ,m.”
BackgroundMethodInfluential
Bayesian Meta-Prior Learning Using Empirical Bayes
Nabi, S., Nassif, H., Hong, J., Mamani, H., & Imbens, G. W. (2021) · Management Science · doi:10.1287/mnsc.2021.4136 · Cited by 20
“Empirical Bayes (EB) is a known methodology to construct informative priors from early randomized data (Robbins 1955, Efron and Morris 1972, Morris 1983, Berger 1985).”
Method
Software reliability
Soyer, R. (2011) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.159 · Cited by 15
Design and Evaluation among Young Adults of a Financial Literacy Scale Focused on Key Financial Decisions
Prado, S. M. M., Chiluiza, K., Everaert, P. C., & Valcke, M. (2022) · Education Sciences · doi:10.3390/educsci12070460 · Cited by 15
Bayesian mixed-membership models of complex and evolving networks
Fienberg, S. E., Carley, K. M., & Airoldi, E. M. (2006) · Cited by 16
Interval Estimation of Random Effects in Proportional Hazards Models with Frailties
Ha, I., Vaida, F., & Lee, Y. (2013) · Statistical Methods in Medical Research · doi:10.1177/0962280212474059 · Cited by 16
“HL: hierarchical likelihood; FMs: frality models; AIC: Akaike information criterion; FM0: Cox model without random effects; FM1: frailty model with one random-center effect; FM2: correlated frailty model with random center and random treatment-by-center interaction (Center-Trt); FM3: correlated frailty model with rand…”
Method
Methods and results for small area estimation using smoking data from the 2008 National Health Interview Survey
Ha, N. S., Lahiri, P., & Parsons, V. L. (2014) · Statistics in Medicine · doi:10.1002/sim.6219 · Cited by 15
“For DEFFi = 1, Carter and Rolph [14] and Morris [15] used models similar to NL1.”
Method
On-demand Reporting of Risk-adjusted and Smoothed Rates for Quality Profiling in ACS NSQIP
Cohen, M. E., Liu, Y., Huffman, K. M., Ko, C. Y., & Hall, B. L. (2016) · Annals of Surgery · doi:10.1097/sla.0000000000001551 · Cited by 15
Bootstrap adjustments for empirical bayes interval estimates of small-area proportions
Farrell, P. J., MacGibbon, B., & Tomberlin, T. J. (1997) · Canadian Journal of Statistics · doi:10.2307/3315358 · Cited by 15
“Several ways have been suggested to correct for this deficiency (see Carlin and Gelfand 1990, 1991; Cox 1975; Laird and Louis 1987; Morris 1983).”
Statistical analysis of outcomes from repeated pregnancies: Effects of HLA sharing on fetal loss rates
Hauck, W. W., Ober, C., Rao, D. C., & Vogler, G. P. (1991) · Genetic Epidemiology · doi:10.1002/gepi.1370080305 · Cited by 15
Optimal Assignment of Bureaucrats: Evidence from Randomly Assigned Tax Collectors in the DRCPreprint
Bergeron, A., Bessone, P., Kabeya, J. K., Tourek, G., & Weigel, J. (2022) · SSRN Electronic Journal · doi:10.3386/w30413 · Cited by 18
Exploration of empirical Bayes hierarchical modeling for the analysis of genome-wide association study data
Heron, E. A., O'Dushlaine, C. T., Segurado, R., Gallagher, L., & Gill, M. (2011) · Biostatistics · doi:10.1093/biostatistics/kxq072 · Cited by 14
Treatment effect heterogeneity for univariate subgroups in clinical trials: Shrinkage, standardization, or else
Varadhan, R., & Wang, S. (2015) · Biometrical Journal · doi:10.1002/bimj.201400102 · Cited by 14
“Following Morris (1983), the empirical Bayes estimate for the multivariate subgroup-specific treatment effect estimates for λ j is λ̂ j = ( 1 − B̂ j ) Qj + B̂ j θ̂ (3) with B̂ j = [(g − 3)/(g − 1)] × σ 2j / (σ 2j + ̂), θ̂ = g∑ j=1 wj Qj / g∑ j=1 wj , and, wj = (σ 2j + )−1, g > 3, ̂ = max ⎧⎨ ⎩ 0, ⎡…”
BackgroundMethodInfluential
Small‐scale Inference: Empirical Bayes and Confidence Methods for as Few as a Single Comparison
Bickel, D. R. (2014) · International Statistical Review · doi:10.1111/insr.12064 · Cited by 14
How to Use Economic Theory to Improve Estimators: Shrinking Toward Theoretical Restrictions
Fessler, P., & Kasy, M. (2018) · The Review of Economics and Statistics · doi:10.1162/rest_a_00795 · Cited by 14
“Parametric empirical Bayes was introduced by Morris (1983).”
BackgroundMethodInfluential
Methods for Accounting for Co-Teaching in Value-Added Models
Hock, H., & Isenberg, E. (2016) · Statistics and Public Policy · doi:10.1080/2330443x.2016.1265473 · Cited by 14
“We applied an empirical Bayes shrinkage procedure based on Morris (1983) to offset the possibility that teachers with few students (or students whose post-test scores were hard to predict based on their characteristics) would be distributed in the tails of the distribution due to chance.”
Method
Priors about observables in vector autoregressions
Jarociński, M., & Marcet, A. (2019) · Journal of Econometrics · doi:10.1016/j.jeconom.2018.12.023 · Cited by 14
“The advantages and disadvantages of this approach have been discussed at length in the literature, see Morris (1983) for a classical reference or Efron (2010) for a more recent reference.”
BackgroundMethod
Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball
Powers, S., Hastie, T. J., & Tibshirani, R. J. (2018) · Statistical Modelling · doi:10.1177/1471082x18777669 · Cited by 14
“Due to Nesterov (2007), this procedure converges with step size s ∈ (0, 1/L) if the log-likelihood ` is continuously differentiable and has Lipschitz gradient with Lipschitz constant L.”
Influential
Parallel tempered trans-dimensional Bayesian inference for the inversion of ultra-deep directional logging-while-drilling resistivity measurements
Shen, Q., Chen, J., Wu, X., Han, Z., & Huang, Y. (2020) · Journal of Petroleum Science and Engineering · doi:10.1016/j.petrol.2020.106961 · Cited by 14
Adjunctive treatment with psychostimulants and stimulant-like drugs for resistant bipolar depression: a systematic review and meta-analysis
Tsapakis, E.-M., Preti, A., Mintzas, M. D., & Fountoulakis, K. Ν. (2020) · CNS Spectrums · doi:10.1017/s109285292000156x · Cited by 15
Empirical Bayes False Coverage Rate Controlling Confidence Intervals
Zhao, Z., & Hwang, J. T. G. (2012) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2012.01033.x · Cited by 14
“We establish that, under certain conditions, the Bayes FCR can be uniformly controlled asymptotically as the number of parameters p (the number of genes) goes to ∞ if the empirical Bayes confidence intervals in the sense of Morris (1983) are used.”
Background
Modeling heavy-tailed correlated noise with wavelet packet basis functions
Gendron, P. J., & Nandram, B. (2002) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(02)00326-9 · Cited by 14
A new class of average moment matching priors
Ganesh, N., & Lahiri, P. (2008) · Biometrika · doi:10.1093/biomet/asn008 · Cited by 14
“This prior specification for the hyperparameters is often recommended; see Berger (1985) and Morris (1983b).”
BackgroundMethod
Estimation of Bowhead Whale, Balaena mysticetus, Population Size
Raftery, A. E., & Zeh, J. E. (1993) · Lecture notes in statistics · doi:10.1007/978-1-4612-2714-4_4 · Cited by 14
A comparison of robust bayes and classical estimators for regional lake models of fish response to acidification
Reckhow, K. H. (1988) · Water Resources Research · doi:10.1029/wr024i007p01061 · Cited by 14
Extension of the Stein Estimating Procedure through the Use of Estimating Functions
Liang, K., & Waclawiw, M. A. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476217 · Cited by 14
EMPIRICAL BAYES METHODS: A TOOL FOR EXPLORATORY ANALYSIS
Braun, H. I. (1989) · Elsevier eBooks · doi:10.1016/b978-0-12-108840-8.50006-8 · Cited by 14
An Experimental Approach to Merger Evaluation
Conlon, C. T., & Mortimer, J. H. (2013) · National Bureau of Economic Research · doi:10.3386/w19703 · Cited by 13
“The development of Empirical Bayes shrinkage is attributed to Morris (1983) and has been widely used in applied microeconomics to shrink outliers from a distribution of fixed effects in teacher value added10 or hospital quality.11 An estimator based on Assn 1 and 2 would be considered a Bayesian…”
Simple and Credible Value-Added Estimation Using Centralized School Assignment
Angrist, J. D., Hull, P., Pathak, P. A., & Walters, C. (2020) · National Bureau of Economic Research · doi:10.3386/w28241 · Cited by 14
“As in Morris (1983), an empirical Bayes estimator based on OLS plugs estimates of σ(2) α and sj into equation (24).”
Physician Practice Style and Healthcare Costs: Evidence from Emergency Departments
Gowrisankaran, G., Joiner, K., & Léger, P. T. (2022) · Management Science · doi:10.1287/mnsc.2022.4544 · Cited by 13
Release of a Regular Version of the Web System of Small Area Population Projections for the Whole Japan
Inoue, T. (2018) · E-journal GEO · doi:10.4157/ejgeo.13.87 · Cited by 13
CAncer bioMarker Prediction Pipeline (CAMPP)—A standardized framework for the analysis of quantitative biological data
Terkelsen, T., Krogh, A., & Papaleo, E. (2020) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1007665 · Cited by 14
Optimal Shrinkage Estimation in Heteroscedastic Hierarchical Linear Models
Kou, S. C., & Yang, J. (2017) · Contributions to statistics · doi:10.1007/978-3-319-41573-4_13 · Cited by 13
“See [15] and [16] for more discussions.”
Background
Empirical Bayes Confidence Intervals for Selected Parameters in High-Dimensional Data
Hwang, J. T. G., & Zhao, Z. (2013) · Journal of the American Statistical Association · doi:10.1080/01621459.2013.771102 · Cited by 13
Estimation of the helium ion density distribution in the plasmasphere based on a single IMAGE/EUV image
Nakano, S., Fok, M., Brandt, P. C., & Higuchi, T. (2014) · Journal of Geophysical Research Space Physics · doi:10.1002/2013ja019733 · Cited by 13
“One way to tune the parameter in the prior distribution is the empirical Bayes method [e.g., Morris, 1983] which evaluates the marginal likelihood defined as follows: p(𝐲|𝜉L, 𝜉𝜙) = ∫ p(𝐲|𝐧eq, 𝜉L, 𝜉𝜙) p(𝐧eq|𝜉L, 𝜉𝜙)d𝐧eq.”
An empirical bayes estimator of seismic events using wavelet packet bases
Gendron, P. J., & Nandram, B. (2001) · Journal of Agricultural Biological and Environmental Statistics · doi:10.1198/108571101317096587 · Cited by 13
Improved minimax estimation of a multivariate normal mean under heteroscedasticity
Tan, Z. (2015) · Bernoulli · doi:10.3150/13-bej580 · Cited by 13
Double shrinkage empirical Bayesian estimation for unknown and unequal variances
Zhao, Z. (2010) · Statistics and Its Interface · doi:10.4310/sii.2010.v3.n4.a11 · Cited by 13
“However, all the literature listed above either assume a known variance σ2 or simply replace them by S2i when σ2i ’s are unknown and unequal (See also Efron and Morris (1973); Morris (1983b)).”
Background
A note on the empirical Bayes heterogeneity variance estimator in meta‐analysis
Sidik, K., & Jonkman, J. N. (2019) · Statistics in Medicine · doi:10.1002/sim.8197 · Cited by 13
“Note that the M-estimation method in this paper leads to two different variance estimators for μŵ, the model-based sandwich variance estimator (7) and the empirical sandwich variance estimator (9).”
Method
An Approximate Bivariate Bayesian Method for Analyzing Small Frequencies
Desouza, C. M. (1992) · Biometrics · doi:10.2307/2532703 · Cited by 14
“In empirical Bayes methodology (Morris, 1983), t is estimated by marginal maximum likelihood or some variant and inferences about (0Oil, 02,) are based on their conditional posterior means, conditional on A, with t equal to its estimated value.”
BackgroundMethod
Empirical Bayes Estimation for the Finite Population Mean on the Current Occasion
Nandram, B., & Sedransk, J. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10476367 · Cited by 13
Estimation of arrest careers using hierarchical stochastic models
Ahn, C. W., Blumstein, A., & Schervish, M. J. (1990) · Journal of Quantitative Criminology · doi:10.1007/bf01065848 · Cited by 13
“An excellent survey of hierarchical models is presented by Morris (1983) .”
Background
TOWARD A MORE APPROPRIATE CONCEPTUALIZATION OF RESEARCH ON SCHOOL EFFECTS: A THREE-LEVEL HIERARCHICAL LINEAR MODEL11The research reported here has been supported by grants from the Spencer Foundation and the Benton Center for Curriculum and Instruction at the University of Chicago. The authors wish to acknowledge the gracious assistance of David Myers in making a small subset of his Sustaining Effects data files available to us for this analysis. The authors also wish to thank Michael Seltzer for his thoughtful comments on an earlier draft of this manuscript.
Bryk, A. S., & Raudenbush, S. W. (1989) · Elsevier eBooks · doi:10.1016/b978-0-12-108840-8.50014-7 · Cited by 13
Inference and decision for set identified parameters using posterior lower and upper probabilities
Kitagawa, T. (2011) · doi:10.1920/wp.cem.2011.1611 · Cited by 13
“This result is well known in the literature (Barankin (60), Florens and Mouchart (74), Picci (77), Dawid (1979), Poirier (1998), among many others), and it can be interpreted that the data only allows us to revise belief on the su¢ cient parameters , while it does not for the conditional prior of given .”
Method
Does the Punishment Fit the Crime? Speeding Fines and RecidivismPreprint
Goncalves, F., & Mello, S. (2017) · SSRN Electronic Journal · doi:10.2139/ssrn.3064406 · Cited by 13
A Bayesian framework for unifying data cleaning, source separation and imaging of electroencephalographic signalsPreprint
Ojeda, A., Klug, M., Kreutz-Delgado, K., Gramann, K., & Mishra, J. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/559450 · Cited by 13
“The PEB/SBL framework for EEG/MEG has been proposed for recovering instantaneous responses in the context of event-related potential (ERP) experiments (Owen et al., 2012; Henson et al., 2011; Friston et al., 2008).”
Method
Small Area Estimation of Non-Monetary Poverty with Geospatial Data
Masaki, T., Newhouse, D., Silwal, A. R., Bedada, A., & Engstrom, R. N. (2020) · World Bank, Washington, DC eBooks · doi:10.1596/1813-9450-9383 · Cited by 14
A Physics-Informed Deep Neural Network for Harmonization of CT Images
Zarei, M., Sotoudeh‐Paima, S., McCabe, C., Abadi, E., & Samei, E. (2024) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2024.3428399 · Cited by 12
Combinational Effects of Clinical Area and Healthcare Workers’ Job Type on the Safety Culture in Hospitals
Jeong, H. J. (2015) · Biometrics & Biostatistics International Journal · doi:10.15406/bbij.2015.02.00024 · Cited by 12
Resisting the extortion racket: an empirical analysis
Battisti, M., Lavezzi, A. M., Masserini, L., & Pratesi, M. (2018) · European Journal of Law and Economics · doi:10.1007/s10657-018-9589-4 · Cited by 12
“However, empirical Bayes prediction (Efron and Morris, 1973 and 1975; Morris, 1983; Maritz and Lwin, 1989; Carlin and Louis, 2000a and 2000b) is the most widely used method for assigning values to random effects.”
BackgroundMethod
Point estimation following two‐stage adaptive threshold enrichment clinical trials
Kimani, P., Todd, S., Renfro, L. A., & Stallard, N. (2018) · Statistics in Medicine · doi:10.1002/sim.7831 · Cited by 12
“The resulting posterior is multivariate normal with nonzero covariance, and hence, the iterative procedure of Morris 27 and Brüncker et al 28 is utilized to obtain ̂𝜃 s , L 2 (see supplementary material).”
EB and EBLUP in Small Area Estimation
Rao, J. N. K. (2001) · Lecture notes in statistics · doi:10.1007/978-1-4613-0141-7_3 · Cited by 12
The Premises is the Premise: Understanding Off- and On-premises Alcohol Sales Outlets to Improve Environmental Alcohol Prevention Strategies
Chinman, M., Burkhart, Q., Ebener, P., Fan, C.-C., Imm, P., Osilla, K. C., Paddock, S. M., & Wright, A. (2011) · Prevention Science · doi:10.1007/s11121-011-0203-z · Cited by 12
“Each model included a random county-specific intercept term to account for the sample design, correlations among respondents from the same county, and to stabilize estimates for counties with small numbers of observations (Morris 1983).”
Empirical Bayes and semi-Bayes adjustments for a vast number of estimations
Strömberg, U. (2009) · European Journal of Epidemiology · doi:10.1007/s10654-009-9393-0 · Cited by 12
“The empirical Bayes and semi-Bayes confidence intervals become approximate Bayes credibility intervals when N (that is, the total number of SNPs) is large [19].”
Background
Comparing the Quality of Health Care Providers
McClellan, M., & Staiger, D. O. (2000) · Forum for Health Economics & Policy · doi:10.2202/1558-9544.1019 · Cited by 12
Hierarchical bayes forecasts of multinomial dirichlet data applied to coupon redemptions
Lenk, P. (1992) · Journal of Forecasting · doi:10.1002/for.3980110703 · Cited by 12
Hierarchical bayesian modeling with elicited prior information
Steffey, D. (1992) · Communication in Statistics- Theory and Methods · doi:10.1080/03610929208830816 · Cited by 15
The Great Equalizer: Medicare and the Geography of Consumer Financial Strain
Goldsmith-Pinkham, P. S., Pinkovskiy, M. L., & Wallace, J. (2023) · National Bureau of Economic Research · doi:10.3386/w31223 · Cited by 15
Fast and Reliable Quantitative Peptidomics with labelpepmatch
Verdonck, R., Haes, W. D., Cardoen, D., Menschaert, G., Huhn, T., Landuyt, B., Baggerman, G., Boonen, K., Wenseleers, T., & Schoofs, L. (2016) · Journal of Proteome Research · doi:10.1021/acs.jproteome.5b00845 · Cited by 11
Multivariate, heteroscedastic empirical Bayes via nonparametric maximum likelihood
Soloff, J. A., Guntuboyina, A., & Sen, B. (2024) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1093/jrsssb/qkae040 · Cited by 11
“03 46 6v 1 [ m at h. ST ] 8 S ep 2 Efron and Morris (1972a,b, 1973a,b); Morris (1983); Efron (2012, 2014) as well as Johnstone (2019) for a manuscript on estimation in Gaussian sequence models).”
Background
Joint modeling of longitudinal data and discrete-time survival outcome
Qiu, F., Stein, C. M., & Elston, R. C. (2013) · Statistical Methods in Medical Research · doi:10.1177/0962280213490342 · Cited by 11
“A correction term that takes the variability in the estimation of the hyperparameters into account must be added into the naïve estimate [19-23].”
Background

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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Parametric Empirical Bayes Inference: Theory and Applications

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks