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Parametric Empirical Bayes Inference: Theory and Applications
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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“The highly parallel nature of gene expression experiments lends itself to a particular class of statistical methods, called parametric empirical Bayes, that borrow information between genes in a dynamic way (14,15).”
From limma powers differential expression analyses for RNA-sequencing and microarray studies (2015) · cites this paper as [15]
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Hierarchical Models for Educational Data: An Overview
Morris, C. N. (1995) · Journal of Educational and Behavioral Statistics · doi:10.3102/10769986020002190 · Cited by 39
“(Using a flat distribution on [0, o°) for T 2 provides proper posterior distributions, and gives good properties in the equal variance situation, where the method can be studied theoretically [cf. Morris, 1983a].)”
BackgroundMethodResultInfluentialA New Approach to Fitting Linear Models in High Dimensional Spaces
Wang, Y. (2000) · Cited by 39
Predictive Updating Methods with Application to Bayesian Classification
Chen, R., & Liu, J. S. (1996) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1996.tb02089.x · Cited by 39
Is Pitman Closeness a Reasonable Criterion?
Robert, C. P., Hwang, J. T. G., & Strawderman, W. E. (1993) · Journal of the American Statistical Association · doi:10.1080/01621459.1993.10594289 · Cited by 39
“Actually, although the Stein effect has strong justifications for quadratic losses, including the empirical Bayes derivations (Morris 1983; Berger 1985), in the Pitman sense it rather appears as a mathematical epiphenomenon, as the usual controls on the shrinkage function disappear and strange estimators may then domi…”
BackgroundEstimating Bowhead Whale Population Size and Rate of Increase from the 1993 Census
Raftery, A. E., & Zeh, J. E. (1998) · Journal of the American Statistical Association · doi:10.1080/01621459.1998.10473694 · Cited by 39
Bryk, A. S., & Raudenbush, S. W. (1989) · Elsevier eBooks · doi:10.1016/b978-0-12-108840-8.50015-9 · Cited by 39
To What Extent Do Student Perceptions of Classroom Quality Predict Teacher Value Added
Raudenbush, S. W., & Jean, M. (2015) · doi:10.1002/9781119210856.ch6 · Cited by 39
“These can be estimated via the empirical Bayes method (Morris, 1983), but now using the multivariate approach (Raudenbush, Rowan, & Kang, 1991), sometimes known as “multivariate shrinkage.”
MethodTyllianakis, E., & Skuras, D. (2016) · Journal of Environmental Management · doi:10.1016/j.jenvman.2016.08.012 · Cited by 40
Mejia, A. F., Nebel, M. B., Barber, A. D., Choe, A. S., Pekar, J. J., Caffo, B. S., & Lindquist, M. A. (2018) · NeuroImage · doi:10.1016/j.neuroimage.2018.01.029 · Cited by 39
“The empirical Bayes shrinkage estimator of μiðq; q0Þ is given as in Morris (1983) by ~wi;T ðq; q0Þ ¼ λðq; q0ÞwT ðq; q0Þ þ f1 λðq; q0Þgwi;T ðq; q0Þ; where wT ðq; q0Þ ¼ 1n Pn i¼1wi;T ðq; q0Þ is the estimated population average connectivity, and the degree of shrinkage λðq; q0Þ is equal to the ratio…”
Filieri, R., Milone, F. L., Paolucci, E., & Raguseo, E. (2023) · International Journal of Hospitality Management · doi:10.1016/j.ijhm.2023.103461 · Cited by 39
“3 For a more detailed description of the methodologies, see Farronato and Fradkin (2018), Morris (1983), while for Stata see Nichols (2008) and Sacarny (2013).”
MethodAre Mortality Rates for Different Operations Related?
Dimick, J. B., Staiger, D. O., & Birkmeyer, J. D. (2006) · Medical Care · doi:10.1097/01.mlr.0000215898.33228.c7 · Cited by 38
“These integrative measures are a generalization of the standard empiric Bayes (or shrinkage) estimator that places more weight on a hospital’s own mortality rate when the ratio of signal to noise in the mortality estimate is high, but shrinks back toward the population mean when the ratio of signal to noise is low.(14…”
BackgroundJeske, D. R., & Harvallie, D. A. (1988) · Communication in Statistics- Theory and Methods · doi:10.1080/03610928808829672 · Cited by 38
Statistical issues in the analysis of disease mapping data
Pascutto, C., Wakefield, J. C., Best, N., Richardson, S. T., Bernardinelli, L., Staines, A. S., & Elliott, P. (2000) · Statistics in Medicine · doi:10.1002/1097-0258(20000915/30)19:17/18 · Cited by 123
Tate, R. L., & Hokanson, J. E. (1993) · Journal of Personality · doi:10.1111/j.1467-6494.1993.tb01031.x · Cited by 38
Fast Moment-Based Estimation for Hierarchical Models
Perry, P. O. (2016) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12165 · Cited by 39
Variation in Physician Practice Styles within and across Emergency Departments
Parys, J. V. (2016) · PLoS ONE · doi:10.1371/journal.pone.0159882 · Cited by 37
“Fig 1 plots the distributions of physician fixed effects (λj) and physician×experience fixed effects (λjt) after adjusting the estimates using the empirical Bayesian shrinkage method described in Morris (1983) [25].”
Combining Observational and Experimental Datasets Using Shrinkage Estimators
Rosenman, E. T. R., Basse, G., Owen, A. B., & Baiocchi, M. (2023) · Biometrics · doi:10.1111/biom.13827 · Cited by 56
“The standard approach is to use a relaxed notion of interval coverage, known as “Empirical Bayes coverage” (Armstrong et al., 2022; Morris, 1983).”
MethodPrediction in Markovian bulk arrival queues
Armero, C., & Conesa, D. (2000) · Queueing Systems · doi:10.1023/a:1019121506451 · Cited by 37
“Bayes methods (Robbins [33,35], Morris [ 28 ] and Maritz and Lwin [24] are classical references in the subject).”
MethodUsing Subject Test Scores Efficiently to Predict Teacher Value-Added
Lefgren, L. J., & Sims, D. (2012) · Educational Evaluation and Policy Analysis · doi:10.3102/0162373711422377 · Cited by 36
“This corresponds to a regression of the raw math value-added computed using data from period t on the raw reading and math value-added measures constructed from T prior periods, not including the reference period, –t, and is similar to the empirical Bayes’s method outlined by Morris (1983). If our assumptions regardin…”
MethodSchmittlein, D. C. (1989) · The American Statistician · doi:10.1080/00031305.1989.10475651 · Cited by 37
“Alternatively, in an empirical Bayes context, the analyst might observe X-values for a sample of these heterogeneous individuals and use those values to estimate the distribution G(0| y) (Morris 1983).”
BackgroundDatta, G. S., Ghosh, M., Smith, D. D., & Lahiri, P. (2002) · Scandinavian Journal of Statistics · doi:10.1111/1467-9469.t01-1-00143 · Cited by 37
“Morris (1983b) considers such a model.”
InfluentialRaftery, A. E., Lewis, S., & Banfield, J. D. (1991) · doi:10.21236/ada241409 · Cited by 37
Shrinkage Confidence Procedures
Casella, G., & Hwang, J. T. G. (2012) · Statistical Science · doi:10.1214/10-sts319 · Cited by 36
“In contrast, in Morris (1983) only the average length across i was made smaller.”
BackgroundMethodInfluentialEmpirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data
Gu, J., & Koenker, R. W. (2016) · Journal of Applied Econometrics · doi:10.1002/jae.2530 · Cited by 36
A Bayesian Analysis of a Poisson Random Effects Model for Home Run Hitters
Albert, J. H. (1992) · The American Statistician · doi:10.1080/00031305.1992.10475898 · Cited by 36
“Morris (1983) modeled Ty Cobb's seasonal batting averages using a similar quadratic model.”
MethodEmpirical Bayes Estimation of Undercount in the Decennial Census
Cressie, N. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478869 · Cited by 36
Risk of alcoholism and parental history: Gender differences and a possible reporting bias
Crum, R. M., & Harris, E. L. (1996) · Genetic Epidemiology · doi:10.1002/(sici)1098-2272(1996)13:4 · Cited by 17
Unbiased Markov chain Monte Carlo with couplingsPreprint
Jacob, P. E., O'Leary, J., & Atchadé, Y. F. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1708.03625 · Cited by 36
“The data (Zn)n=1 are baseball players’ batting averages taken from Table 1 of Morris [1983], where K = 18.”
MethodJacob, B. A., & Lefgren, L. J. (2005) · National Bureau of Economic Research · doi:10.3386/w11494 · Cited by 36
Small Area Shrinkage Estimation
Datta, G., & Ghosh, M. (2012) · Statistical Science · doi:10.1214/11-sts374 · Cited by 35
Duncan, G. T., Gorr, W. L., & Szczypula, J. (1993) · Management Science · doi:10.1287/mnsc.39.3.275 · Cited by 35
Jackson, D., & Bowden, J. (2016) · BMC Medical Research Methodology · doi:10.1186/s12874-016-0219-y · Cited by 35
“It has recently been shown that the Paule-Mandel and the Empirical Bayes [22, 23] estimators are equivalent in the more general context of random effects models for meta-regression [24].”
BackgroundSmall-Data, Large-Scale Linear Optimization with Uncertain Objectives
Gupta, V., & Rusmevichientong, P. (2020) · Management Science · doi:10.1287/mnsc.2019.3554 · Cited by 35
Bayes, Oracle Bayes and Empirical Bayes
Efron, B. (2019) · Statistical Science · doi:10.1214/18-sts674 · Cited by 35
“Morris (1983) provided a normality-based theory of empirical Bayes confidence intervals.”
Improved Estimates of Cancer Site-Specific Risks for A-Bomb Survivors
Pawel, D. J., Preston, D. L., Pierce, D. A., & COLOGNE, J. B. (2007) · Radiation Research · doi:10.1667/rr1092.1 · Cited by 35
“This approach has long been used successfully in many fields, such as estimation of product quality (1), geological reserves (2), abilities of individual athletes (3), calculation of insurance premiums (4), small area estimation from sample surveys (5), and most classically, selection of sires for breeding genetics (6…”
BackgroundAssessing surrogacy of data sources for institutional comparisons
Normand, S. T., Wang, Y., & Krumholz, H. M. (2007) · Health Services and Outcomes Research Methodology · doi:10.1007/s10742-006-0018-8 · Cited by 35
“However the estimates were based on shrinkage procedures that do increase the effective sample size for each unit (Morris 1983).”
MethodRandom effects and shrinkage estimation in capture-recapture models
Royle, J. A., & Link, W. A. (2002) · Journal of Applied Statistics · doi:10.1080/02664760120108746 · Cited by 35
“In this regard, there is an old metaphor attributed by Morris (1983, rejoinder) to Savage (1961) which refers to considering parameters to be random as `breaking the Bayesian egg’ and posterior inference as `enjoying the omelette’ that results from breaking that egg.”
BackgroundHealthcare Exceptionalism? Productivity and Allocation in the U.S. Healthcare Sector
Chandra, A., Finkelstein, A. N., Sacarny, A., & Syverson, C. (2013) · National Bureau of Economic Research · doi:10.3386/w19200 · Cited by 34
Empirical Bayes Confidence Intervals Shrinking Both Means and Variances
Hwang, J. T. G., Qiu, J., & Zhao, Z. (2008) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.1467-9868.2008.00681.x · Cited by 34
“Unlike in Qiu and Hwang (2007), there is no exact solution to the approximated equation (6.”
BackgroundMethodBid Takers or Market Makers? The Effect of Auctioneers on Auction Outcome
Lacetera, N., Larsen, B., Pope, D. G., & Sydnor, J. (2016) · American Economic Journal Microeconomics · doi:10.1257/mic.20150020 · Cited by 31
Likelihood Inference for Models with Unobservables: Another View
Lee, Y., & Nelder, J. A. (2009) · Statistical Science · doi:10.1214/09-sts277 · Cited by 34
Parametric Empirical Bayes Methods for Ecological Applications
Hoef, J. M. V. (1996) · Ecological Applications · doi:10.2307/2269589 · Cited by 34
Employing vague prior information in the construction of confidence sets
Casella, G., & Hwang, J. T. (1987) · Journal of Multivariate Analysis · doi:10.1016/0047-259x(87)90100-x · Cited by 34
Raudenbush, S. W. (2007) · Handbook of Multilevel Analysis · doi:10.1007/978-0-387-73186-5_5 · Cited by 51
Confidence sets centered at James—Stein estimators
Hwang, J. T. G., & Ullah, A. (1994) · Journal of Econometrics · doi:10.1016/0304-4076(94)90041-8 · Cited by 33
A Probabilistic Model for Canonicalizing Named Entity Mentions
Yogatama, D., Sim, Y., & Smith, N. A. (2018) · Figshare · doi:10.1184/r1/6472979 · Cited by 33
Empirical Bayes methods in classical and Bayesian inference
Petrone, S., Rizzelli, S., Rousseau, J., & Scricciolo, C. (2014) · METRON · doi:10.1007/s40300-014-0044-1 · Cited by 33
“As discussed by Morris [29], parametric empirical Bayes procedures are needed to deal with those cases where n is too small to well approximate the Bayesian solution, but still a substantial improvement over standard methods can be made as for the James–Stein’s estimator.”
MethodGrund, S., Lüdtke, O., & Robitzsch, A. (2017) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998617738087 · Cited by 33
“This approach is similar to obtaining “empirical Bayes” estimates for random effects in multilevel modeling (e.g., Laird & Ware, 1982; Morris, 1983).”
MethodModel selection for the North American Breeding Bird Survey
Link, W. A., Sauer, J. R., & Niven, D. K. (2020) · Ecological Applications · doi:10.1002/eap.2137 · Cited by 33
Bayesian reliability models of Weibull systems: State of the art
Zaïdi, A., Bouamama, B. O., & Tagina, M. (2012) · International Journal of Applied Mathematics and Computer Science · doi:10.2478/v10006-012-0045-2 · Cited by 33
“In the literature, there is a significant number of papers explaining this theory and the logic of its use as well as the relationships to the other statistical techniques (Casella, 1985; Deely and Lindley, 1981; Morris, 1983).”
BackgroundCondition Numbers and Minimax Ridge Regression Estimators
Casella, G. (1985) · Journal of the American Statistical Association · doi:10.1080/01621459.1985.10478180 · Cited by 33
A bibliography and comments on the use of statistical models in epidemiology in the 1980s
Gail, M. H. (1991) · Statistics in Medicine · doi:10.1002/sim.4780101204 · Cited by 33
Waldman, I. D., Robinson, B. F., & Feigon, S. A. (1997) · Genetic Epidemiology · doi:10.1002/(sici)1098-2272(1997)14:6 · Cited by 60
Review and Synthesis of Estimation Strategies to Meet Small Area Needs in Forest Inventory
Dettmann, G. T., Radtke, P. J., Coulston, J. W., Green, P. C., Wilson, B. T., & Moisen, G. G. (2022) · Frontiers in Forests and Global Change · doi:10.3389/ffgc.2022.813569 · Cited by 32
“Bayesian methods have been applied to SAE across disciplines for several decades (Morris, 1983; Ghosh and Rao, 1994), with recent applications in forest inventory settings as well (e.g., Finley et al., 2011).”
MethodHasan, S., de Mheen, P. J. M., Kaptein, B. L., Nelissen, R. G. H. H., & Pijls, B. G. C. W. (2020) · Clinical Orthopaedics and Related Research · doi:10.1097/corr.0000000000001209 · Cited by 32
“In a sensitivity analysis, the more conservative empirical Bayes estimator was used to test whether the heterogeneity estimator would affect the results [23].”
MethodCredible School Value-Added with Undersubscribed School Lotteries
Angrist, J. D., Hull, P., Pathak, P. A., & Walters, C. (2021) · The Review of Economics and Statistics · doi:10.1162/rest_a_01149 · Cited by 32
Fee Variation in Private Equity
Begenau, J., & SIRIWARDANE, E. N. (2024) · The Journal of Finance · doi:10.1111/jofi.13319 · Cited by 32
Modeling hypoxia in the Chesapeake Bay: Ensemble estimation using a Bayesian hierarchical model
Stow, C. A., & Scavia, D. (2008) · Journal of Marine Systems · doi:10.1016/j.jmarsys.2008.05.008 · Cited by 33
“Ensemble estimation is based on the premise that, when multiple response variables share common or similar parameters, simultaneous estimation of these parameters yields more precise inference (Congdon, 2001), a result of “borrowing strength from the ensemble” (Morris, 1983).”
BackgroundA computational framework for empirical Bayes inference
Atchadé, Y. F. (2010) · Statistics and Computing · doi:10.1007/s11222-010-9182-3 · Cited by 32
“Keywords and phrases: Empirical Bayes, Adaptive MCMC, Variable selection, Bayesian LASSO.”
MethodAre Female Supervisors More Female-Friendly?
Bednar, S., & Gicheva, D. (2014) · American Economic Review · doi:10.1257/aer.104.5.370 · Cited by 32
Reliability of Essay Rating and Score Adjustment
Longford, N. T. (1994) · Journal of Educational and Behavioral Statistics · doi:10.3102/10769986019003171 · Cited by 32
“The adjustment schemes are based on shrinkage estimators (Morris, 1983) of the true scores.”
BackgroundSmoothing the non-parametric estimate of a prior distribution by roughening
Laird, N. M., & Louis, T. A. (1991) · Computational Statistics & Data Analysis · doi:10.1016/0167-9473(91)90101-7 · Cited by 32
Multilevel assessment of immunisation uptake as a performance measure in general practice.
Jones, K., & Moon, G. (1991) · BMJ · doi:10.1136/bmj.303.6793.28 · Cited by 32
An Overview of the U.S. Census Bureau's Small Area Income and Poverty Estimates Program
Bell, W. R., Basel, W. W., & Maples, J. J. (2016) · doi:10.1002/9781118814963.ch19 · Cited by 32
Worker Beliefs About Outside OptionsPreprint
Jäger, S., Roth, C., Roussille, N., & Schoefer, B. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.3998796 · Cited by 32
Small area estimation: its evolution in five decades
Ghosh, M. (2020) · Statistics in Transition New Series · doi:10.21307/stattrans-2020-022 · Cited by 31
“(Morris, 1983, JASA).”
Evaluation and comparison of estimation methods for failure rates and probabilities
Vaurio, J., & Jänkälä, K. (2006) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2005.01.001 · Cited by 44
Liang, Y., & Kelemen, A. (2005) · Functional & Integrative Genomics · doi:10.1007/s10142-005-0006-z · Cited by 31
“Shrinkage parameters are also called empirical Bayesian parameters and were introduced by Robbins (1955) and further developed by many authors (Efron and Morris 1973, 1975; Morris 1983).”
MethodMultilevel Modeling and its Application in Counseling Psychology Research
Reise, S. P., & Duan, N. (1999) · The Counseling Psychologist · doi:10.1177/0011000099274003 · Cited by 31
“This procedure reduces the overall mean squared error (Efron & Morris, 1975; Morris, 1983).”
MethodEcological and individual effects in childhood immunisation uptake: A multi-level approach
Jones, K., Moon, G., & Clegg, A. J. (1991) · Social Science & Medicine · doi:10.1016/0277-9536(91)90332-7 · Cited by 31
de Valpine, P. (2009) · Ecological Applications · doi:10.1890/08-0562.1 · Cited by 30
Do Low-Income Students Have Equal Access to Effective Teachers?
Isenberg, E., Max, J., Gleason, P., & Deutsch, J. (2021) · Educational Evaluation and Policy Analysis · doi:10.3102/01623737211040511 · Cited by 40
“However, for measuring differences in the proportion of low- and high-income students who have teachers at different percentiles of the distribution of value-added estimates, we applied empirical Bayes shrinkage as a final step using a procedure outlined in Morris (1983).”
MethodInterval Estimation for Messy Observational Data
Gustafson, P., & Greenland, S. (2009) · Statistical Science · doi:10.1214/09-sts305 · Cited by 30
“For instance, the “Ty Cobb” example in Morris (1983) involves explicit modeling of a time trend for parameter values corresponding to consecutive calendar years.”
MethodStudy specific prediction intervals for random‐effects meta‐analysis: A tutorial
van Aert, R. C. M., Schmid, C. H., Svensson, D. J., & Jackson, D. (2021) · Research Synthesis Methods · doi:10.1002/jrsm.1490 · Cited by 33
Penalized likelihood methods improve parameter estimates in occupancy models
Hutchinson, R., Valente, J. J., Emerson, S. C., Betts, M. G., & Dietterich, T. G. (2015) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12368 · Cited by 29
“Our approach of setting k using cross-validation is essentially an empirical Bayes (or TypeII Likelihood) approach (Morris 1983).”
MethodVolman, M. N. M., Rep, A., Kadzinska, I., Berkhof, J. H., van Geijn, H. P., Heethaar, R. M., & de Vries, J. I. P. (2007) · BJOG An International Journal of Obstetrics & Gynaecology · doi:10.1111/j.1471-0528.2007.01300.x · Cited by 29
An empirical hierarchical Bayesian unification of occupational exposure assessment methods
Sottas, P., Lavoué, J., Bruzzi, R., Vernez, D., Charrière, N., & Droz, P. (2008) · Statistics in Medicine · doi:10.1002/sim.3411 · Cited by 29
Assessment of Spatial Variation of Risks in Small Populations
Riggan, W. B., Mantón, K. G., Creason, J. P., Woodbury, M. A., & Stallard, E. (1991) · Environmental Health Perspectives · doi:10.1289/ehp.9196223 · Cited by 29
Empirical Bayes Confidence Intervals for a Series of Related Experiments
Laird, N. M., & Louis, T. A. (1989) · Biometrics · doi:10.2307/2531491 · Cited by 29
Model‐based estimation of vaccine effects from community vaccine trials
Longini, I. M., Halloran, M. E., & Nizam, A. (2002) · Statistics in Medicine · doi:10.1002/sim.994 · Cited by 29
“For these more complex models, hierarchical Bayes empirical methods could be used [24; 25].”
MethodCharter Schools and Labor Market Outcomes
Dobbie, W., & Fryer, R. G. (2016) · National Bureau of Economic Research · doi:10.3386/w22502 · Cited by 31
Woods, C. M., Oltmanns, T. F., & Turkheimer, E. N. (2008) · Psychological Assessment · doi:10.1037/1040-3590.20.2.159 · Cited by 28
Fixed and random effects models
Gurka, M. J., Kelley, G. A., & Edwards, L. J. (2011) · Wiley Interdisciplinary Reviews Computational Statistics · doi:10.1002/wics.201 · Cited by 29
Mostafaei, S., Keshavarz, M., Nahand, J. S., Hassankiadeh, R. F., Moradinazar, M., Nouri, M., Babaei, F., Ahadi, M., Payandeh, M., Esker, A. S., et al. (2020) · Pathology - Research and Practice · doi:10.1016/j.prp.2020.152855 · Cited by 28
Empirical Bayes in-season prediction of baseball batting averages
Jiang, W., & Zhang, C. (2010) · Institute of Mathematical Statistics collections · doi:10.1214/10-imscoll618 · Cited by 28
“A parametric empirical Bayes method, as defined in [13], approximates”
MethodBayesian Approaches to Meta-analysi of ROC Curves
Hellmich, M., Abrams, K. R., & Sutton, A. J. (1999) · Medical Decision Making · doi:10.1177/0272989x9901900304 · Cited by 28
A SIMPLE MONTE CARLO APPROACH TO BAYESIAN GRADUATION
Carlin, B. P. (1992) · Cited by 28
Empirical bayes estimators for spatially correlated incidence rates
Devine, O. J., Louis, T. A., & Halloran, M. E. (1994) · Environmetrics · doi:10.1002/env.3170050403 · Cited by 28
Access to Effective Teaching for Disadvantaged StudentsPreprint
Isenberg, E., Max, J. E., Gleason, P., Potamites, L., Santillano, R., Hock, H., & Hansén, M. (2013) · RePEc: Research Papers in Economics · Cited by 28
The Impact of Organizational Boundaries on Health Care Coordination and Utilization
Agha, L., Ericson, K. M. M., & Zhao, X. (2023) · American Economic Journal Economic Policy · doi:10.1257/pol.20200841 · Cited by 28
Les modèles linéaires hiérarchiques : 1. principes et illustration
Arrègle, J.-L. (2003) · M n gement · doi:10.3917/mana.061.0001 · Cited by 27
“L’estimateur bayesien est aussi qualifié de shrinkage estimator (James et Stein, 1961; Morris, 1983).”
BackgroundA second-order efficient empirical Bayes confidence interval
Yoshimori, M., & Lahiri, P. (2014) · The Annals of Statistics · doi:10.1214/14-aos1219 · Cited by 27
“For the same two level model, flat prior distribution on A is widely accepted [see Morris and Tang (2011)].”
BackgroundMethodInfluentialAnalysis of Multiple Exposures
Momoli, F., Abrahamowicz, M., Parent, M., Krewski, D., & Siemiatycki, J. (2009) · Epidemiology · doi:10.1097/ede.0b013e3181c297c7 · Cited by 27
Empirical Bayes Combination of Estimated Areas under ROC Curves Using Estimating Equations
Zhou, X. (1996) · Medical Decision Making · doi:10.1177/0272989x9601600109 · Cited by 27
Bayesian analysis of non‐homogeneous Markov chains: Application to mental health data
Sung, M., Soyer, R., & Nhan, N. C. T. (2006) · Statistics in Medicine · doi:10.1002/sim.2775 · Cited by 27
“An empirical Bayes approach is introduced by Meshkani [10] for homogenous chains who considered extensions to nonhomogeneous Markov chains by viewing the problem as a parametric empirical Bayes problem in the sense of Morris [11].”
MethodHierarchically-coupled hidden Markov models for learning kinetic rates from single-molecule data
van de Meent, J., Bronson, J. E., Wood, F. D., Gonzalez, R. L., & Wiggins, C. (2013) · International Conference on Machine Learning · doi:10.48550/arxiv.1305.3640 · Cited by 33
“The hyperparameters are estimated with an empirical Bayes approach (Morris, 1983).”
BackgroundMethodInfluentialOptimal shrinkage estimation of mean parameters in family of distributions with quadratic variance
Xie, X., Kou, S. C., & Brown, L. (2016) · The Annals of Statistics · doi:10.1214/15-aos1377 · Cited by 27
“For applications of shrinkage techniques in practice, see Efron and Morris (1975), Rubin (1981), Morris (1983), Green and Strawderman (1985), Jones (1991) and Brown (2008).”
MethodLearning from a lot: Empirical Bayes for high‐dimensional model‐based prediction
van de Wiel, M. A., Beest, D. E. T., & Münch, M. (2018) · Scandinavian Journal of Statistics · doi:10.1111/sjos.12335 · Cited by 31
“In the low-dimensional Bayesian linear regression setting, Morris (1983) and Basu, Ghosh, and Mukerjee (2003) provide theoretical guarantees for the coverage of an EB interval, which accounts for the uncertainty of the prediction and the shrinkage factor.”
InfluentialEvaluation and Comparison of Estimation Methods for Failure Rates and Probabilities
Vaurio, J. K., & Jänkälä, K. E. (2004) · Springer eBooks · doi:10.1007/978-0-85729-410-4_54 · Cited by 27
Multilevel Modeling of Cognitive Function in Schizophrenic Patients and Their First Degree Relatives
Rabe‐Hesketh, S., Toulopoulou, T., & Murray, R. M. (2001) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3602_07 · Cited by 27
“…variables, P[u 0i | {Y ij } , x ij ], may be obtained by applying Bayes Theorem and the random effects are estimated by their conditional expectations (4) E u Y u P u Y dui ij ij i i ij ij i[ ] [ ]0 0 0 0| , | ,n s n sx x= z known as empirical Bayes estimates (see for example Morris, 1983).”
BackgroundMethod
Metadata
- 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
- 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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