Inference for Multivariate Normal Hierarchical Models

Everson, Philip J.; Morris, Carl N.

doi:10.1111/1467-9868.00239

Cited by 107Statistical Methods and Bayesian InferenceMarkov Chains and Monte Carlo MethodsBayesian Methods and Mixture Models

Inference for Multivariate Normal Hierarchical Models

Everson, Philip J., Morris, Carl N.·2000·Journal of the Royal Statistical Society Series B: Statistical Methodology

DOI 10.1111/1467-9868.00239

Open this paper in CoChat — free account

Abstract

Summary: This paper provides a new method and algorithm for making inferences about the parameters of a two-level multivariate normal hierarchical model. One has observed J p-dimensional vector outcomes, distributed at level 1 as multivariate normal with unknown mean vectors and with known covariance matrices. At level 2, the unknown mean vectors also have normal distributions, with common unknown covariance matrix A and with means depending on known covariates and on unknown regression coefficients. The algorithm samples independently from the marginal posterior distribution of A by using rejection procedures. Functions such as posterior means and covariances of the level 1 mean vectors and of the level 2 regression coefficient are estimated by averaging over posterior values calculated conditionally on each value of A drawn. This estimation accounts for the uncertainty in A, unlike standard restricted maximum likelihood empirical Bayes procedures. It is based on independent draws from the exact posterior distributions, unlike Gibbs sampling. The procedure is demonstrated for profiling hospitals based on patients' responses concerning p=2 types of problems (non-surgical and surgical). The frequency operating characteristics of the rule corresponding to a particular vague multivariate prior distribution are shown via simulation to achieve their nominal values in that setting.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Integrity signals

Registry

Crossref · 10.1111/1467-9868.00239

Cites

27 of 27 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Hierarchical Linear Models: Applications and Data Analysis Methods.
Longford, N. T., Bryk, A. S., & Raudenbush, S. W. (1993) · Contemporary Sociology A Journal of Reviews · doi:10.2307/2075823 · Cited by 18,768 · see citing works
Sampling-based approaches to calculating marginal densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10476213 · Cited by 6,606 · see citing works
The Calculation of Posterior Distributions by Data Augmentation
Tanner, M. A., & Wong, W. H. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478458 · Cited by 3,929 · see citing works
Hierarchical Linear Models: Applications and Data Analysis Methods.
Goldstein, H., Bryk, A. S., & Raudenbush, S. W. (1993) · Journal of the American Statistical Association · doi:10.2307/2290750 · Cited by 3,320 · see citing works
Multilevel Statistical Models
Courgeau, D., & Goldstein, H. (1997) · Population · doi:10.2307/1534624 · Cited by 2,590 · see citing works
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 · see citing works
Stochastic Simulation
Ripley, B. D. (1987) · Wiley Series in Probability and Statistics · doi:10.1002/9780470316726 · Cited by 2,241 · see citing works
Bayes and Empirical Bayes Methods for Data Analysis
Carlin, B. P., & Louis, T. A. (2001) · Technometrics · doi:10.1198/tech.2001.s608 · Cited by 2,110 · see citing works
Sampling-Based Approaches to Calculating Marginal Densities
Gelfand, A. E., & Smith, A. F. M. (1990) · Journal of the American Statistical Association · doi:10.2307/2289776 · Cited by 1,531 · see citing works
Parametric empirical Bayes inference: theory and applications
Morris, C. N. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10477920 · Cited by 1,448 · see citing works
Self-citation
Bayesian Forecasting and Dynamic Models
West, M., & Harrison, J. (1989) · Springer series in statistics · doi:10.1007/978-1-4757-9365-9 · Cited by 1,318 · see citing works
Random Coefficient Models
Longford, N. T. (2011) · International Encyclopedia of Statistical Science · doi:10.1007/978-3-642-04898-2_471 · Cited by 751 · see citing works
Bayesian Forecasting and Dynamic Models (2nd edn)
Wheeler, F. P. (1998) · Journal of the Operational Research Society · doi:10.1057/palgrave.jors.2600494 · Cited by 678 · see citing works
Bayes and Empirical Bayes Methods for Data Analysis
Rukhin, A. L., Carlin, B. P., & Louis, T. A. (1997) · Technometrics · doi:10.2307/1271144 · Cited by 454 · see citing works
Estimation in Covariance Components Models
Dempster, A. P., Rubin, D. B., & Tsutakawa, R. K. (1981) · Journal of the American Statistical Association · doi:10.1080/01621459.1981.10477653 · Cited by 444 · see citing works
Random Coefficient Models
Longford, N. T. (1994) · doi:10.1093/oso/9780198522645.001.0001 · Cited by 399 · see citing works
Empirical Bayes on vector observations: An extension of Stein's method
Efron, B., & Morris, C. N. (1972) · Biometrika · doi:10.1093/biomet/59.2.335 · Cited by 224 · see citing works
Self-citation
Hierarchical Poisson Regression Modeling
Christiansen, C. L., & Morris, C. N. (1997) · Journal of the American Statistical Association · doi:10.1080/01621459.1997.10474013 · Cited by 165 · see citing works
Self-citation
A Numerical Procedure to Generate a Sample Covariance Matrix
Odell, P. L., & Feiveson, A. H. (1966) · Journal of the American Statistical Association · doi:10.1080/01621459.1966.10502018 · Cited by 156 · see citing works
Matrix Algebra Useful for Statistics.
Ling, R. F., & Searle, S. R. (1984) · Journal of the American Statistical Association · doi:10.2307/2288737 · Cited by 128 · see citing works
Stochastic Simulation
Booker, J. M., & Ripley, B. D. (1988) · Technometrics · doi:10.1080/00401706.1988.10488373 · Cited by 127 · see citing works
Fast EM-type Implementations for Mixed Effects Models
Meng, X.-L., & van Dyk, D. A. (1998) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00140 · Cited by 105 · see citing works
Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution
Hwang, J. T., & Casella, G. (1982) · The Annals of Statistics · doi:10.1214/aos/1176345877 · Cited by 96 · see citing works
Parametric Empirical Bayes Confidence Intervals
Morris, C. N. (1983) · Elsevier eBooks · doi:10.1016/b978-0-12-121160-8.50008-9 · Cited by 83 · see citing works
Self-citation
Empirical Bayes Confidence Sets for the Mean of a Multivariate Normal Distribution
Casella, G., & Hwang, J. T. (1983) · Journal of the American Statistical Association · doi:10.1080/01621459.1983.10478030 · Cited by 56 · see citing works
Meta-Analysis Software: A Comparative Review
Normand, S. T. (1995) · The American Statistician · doi:10.1080/00031305.1995.10476170 · Cited by 26 · see citing works
Simulation from Wishart Distributions with Eigenvalue Constraints
Everson, P. J., & Morris, C. N. (2000) · Journal of Computational and Graphical Statistics · doi:10.2307/1390660 · Cited by 11 · see citing works
Self-citation

Flagged first, then by citations

1 of the 28 references couldn’t be matched to a known paper.

Research works printed but not linked: 2

Everson, P. (1995) Inference for multivariate normal hierarchical models. PhD Dissertation. Department of Statistics, Harvard University, Cambridge.
Hox, J. (1998) Multilevel modeling in windows: a review of MLWin. Multilev Modllng Newslett., 10, no. 2, 2±5.

Sorted by citations

Fine Particulate Air Pollution and Hospital Admission for Cardiovascular and Respiratory Diseases
Dominici, F., Peng, R. D., Bell, M. L., Pham, L. D., McDermott, A., Zeger, S. L., & Samet, J. M. (2006) · JAMA · doi:10.1001/jama.295.10.1127 · Cited by 2,640 · see citing works
Weather-Related Mortality
Anderson, B. G., & Bell, M. L. (2009) · Epidemiology · doi:10.1097/ede.0b013e318190ee08 · Cited by 1,233 · see citing works
Heat Waves in the United States: Mortality Risk during Heat Waves and Effect Modification by Heat Wave Characteristics in 43 U.S. Communities
Anderson, G. B., & Bell, M. L. (2011) · Environmental Health Perspectives · doi:10.1289/ehp.1002313 · Cited by 1,191 · see citing works
Heat Effects on Mortality in 15 European Cities
Baccini, M., Biggeri, A., Accetta, G., Kosatsky, T., Katsouyanni, K., Analitis, A., Anderson, H. R., Bisanti, L., D’Ippoliti, D., Dáňová, J., et al. (2008) · Epidemiology · doi:10.1097/ede.0b013e318176bfcd · Cited by 887 · see citing works
Model Choice in Time Series Studies of Air Pollution and Mortality
Peng, R. D., Dominici, F., & Louis, T. A. (2006) · Journal of the Royal Statistical Society Series A: Statistics in Society · doi:10.1111/j.1467-985x.2006.00410.x · Cited by 583 · see citing works
Emergency Admissions for Cardiovascular and Respiratory Diseases and the Chemical Composition of Fine Particle Air Pollution
Peng, R. D., Bell, M. L., Geyh, A. S., McDermott, A., Zeger, S. L., Samet, J. M., & Dominici, F. (2009) · Environmental Health Perspectives · doi:10.1289/ehp.0800185 · Cited by 560 · see citing works
The Exposure–Response Curve for Ozone and Risk of Mortality and the Adequacy of Current Ozone Regulations
Bell, M. L., Peng, R. D., & Dominici, F. (2006) · Environmental Health Perspectives · doi:10.1289/ehp.8816 · Cited by 481 · see citing works
“We fit this two-stage normal–normal model by use of a two-level normal independent sampling estimation (TLNise 2006) with noninformative priors (Everson and Morris 2000).”
Influential
Hospital Admissions and Chemical Composition of Fine Particle Air Pollution
Bell, M. L., Ebisu, K., Peng, R. D., Samet, J. M., & Dominici, F. (2009) · American Journal of Respiratory and Critical Care Medicine · doi:10.1164/rccm.200808-1240oc · Cited by 500 · see citing works
Seasonal analyses of air pollution and mortality in 100 US cities
Peng, R. D., Dominici, F., Pastor-Barriuso, R., Zeger, S. L., & Samet, J. M. (2005) · American Journal of Epidemiology · doi:10.1093/aje/kwi075 · Cited by 450 · see citing works
Coarse Particulate Matter Air Pollution and Hospital Admissions for Cardiovascular and Respiratory Diseases Among Medicare Patients
Peng, R. D. (2008) · JAMA · doi:10.1001/jama.299.18.2172 · Cited by 405 · see citing works
Heat-Related Mortality and Adaptation to Heat in the United States
Bobb, J. F., Peng, R. D., Bell, M. L., & Dominici, F. (2014) · Environmental Health Perspectives · doi:10.1289/ehp.1307392 · Cited by 354 · see citing works
Revised Analyses of the National Morbidity, Mortality, and Air Pollution Study: Mortality Among Residents Of 90 Cities
Dominici, F., McDermott, A., Daniels, M. J., Zeger, S. L., & Samet, J. M. (2005) · Journal of Toxicology and Environmental Health · doi:10.1080/15287390590935932 · Cited by 332 · see citing works
Local and Global Effects of Climate on Dengue Transmission in Puerto Rico
Johansson, M. A., Dominici, F., & Glass, G. E. (2009) · PLoS neglected tropical diseases · doi:10.1371/journal.pntd.0000382 · Cited by 329 · see citing works
Air Pollution and Mortality: Estimating Regional and National Dose-Response Relationships
Dominici, F., Daniels, M., Zeger, S. L., & Samet, J. M. (2002) · Journal of the American Statistical Association · doi:10.1198/016214502753479266 · Cited by 303 · see citing works
Heat-related Emergency Hospitalizations for Respiratory Diseases in the Medicare Population
Anderson, G. B., Dominici, F., Wang, Y., McCormack, M. C., Bell, M. L., & Peng, R. D. (2013) · American Journal of Respiratory and Critical Care Medicine · doi:10.1164/rccm.201211-1969oc · Cited by 275 · see citing works
Nonconjugate Bayesian Estimation of Covariance Matrices and Its Use in Hierarchical Models
Daniels, M. J., & Kass, R. E. (1999) · Journal of the American Statistical Association · doi:10.1080/01621459.1999.10473878 · Cited by 220 · see citing works
Particulate Air Pollution and Mortality in the United States: Did the Risks Change from 1987 to 2000?
Dominici, F., Peng, R. D., Zeger, S. L., White, R. H., & Samet, J. M. (2007) · American Journal of Epidemiology · doi:10.1093/aje/kwm222 · Cited by 186 · see citing works
Effect Modification by Community Characteristics on the Short-term Effects of Ozone Exposure and Mortality in 98 US Communities
Bell, M. L., & Dominici, F. (2008) · American Journal of Epidemiology · doi:10.1093/aje/kwm396 · Cited by 183 · see citing works
Health Effects of Air Pollution: A Statistical Review
Dominici, F., Sheppard, L. A., & Clyde, M. A. (2003) · International Statistical Review · doi:10.1111/j.1751-5823.2003.tb00195.x · Cited by 173 · see citing works
Urban residence, neighborhood poverty, race/ethnicity, and asthma morbidity among children on Medicaid
Keet, C. A., Matsui, E. C., McCormack, M. C., & Peng, R. D. (2017) · Journal of Allergy and Clinical Immunology · doi:10.1016/j.jaci.2017.01.036 · Cited by 171 · see citing works
Both low and high temperature may increase the risk of stroke mortality
Chen, R., Wang, C., Meng, X., Chen, H., Thach, T., Wong, C.-M., & Kan, H. (2013) · Neurology · doi:10.1212/wnl.0b013e3182a4a43c · Cited by 170 · see citing works
Improved Semiparametric Time Series Models of Air Pollution and Mortality
Dominici, F., McDermott, A., & Hastie, T. J. (2004) · Journal of the American Statistical Association · doi:10.1198/016214504000000656 · Cited by 169 · see citing works
Bayesian analysis of covariance matrices and dynamic models for longitudinal data
Daniels, M. J. (2002) · Biometrika · doi:10.1093/biomet/89.3.553 · Cited by 167 · see citing works
A prior for the variance in hierarchical models
Daniels, M. J. (1999) · Canadian Journal of Statistics · doi:10.2307/3316112 · Cited by 157 · see citing works
Seasonal variation in the acute effect of particulate air pollution on mortality in the China Air Pollution and Health Effects Study (CAPES)
Chen, R., Peng, R. D., Meng, X., Zhou, Z., Chen, B., & Kan, H. (2013) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2013.02.040 · Cited by 135 · see citing works
A Meta-Analysis and Multisite Time-Series Analysis of the Differential Toxicity of Major Fine Particulate Matter Constituents
Levy, J. I., Diez, D. M., Dou, Y., Barr, C. D., & Dominici, F. (2012) · American Journal of Epidemiology · doi:10.1093/aje/kwr457 · Cited by 125 · see citing works
Mixed beta regression: A Bayesian perspective
Figueroa-Zúñiga, J., Arellano-Valle, R. B., & Ferrari, S. L. P. (2012) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2012.12.002 · Cited by 121 · see citing works
Excessive Heat and Respiratory Hospitalizations in New York State: Estimating Current and Future Public Health Burden Related to Climate Change
Lin, S., Hsu, W.-H., Van Zutphen, A. R., Saha, S., Luber, G., & Hwang, S.-A. (2012) · Environmental Health Perspectives · doi:10.1289/ehp.1104728 · Cited by 105 · see citing works
Bayesian correlation estimation
Liechty, J. (2004) · Biometrika · doi:10.1093/biomet/91.1.1 · Cited by 105 · see citing works
Does the Effect of PM10 on Mortality Depend on PM Nickel and Vanadium Content? A Reanalysis of the NMMAPS Data
Dominici, F., Peng, R. D., Ebisu, K., Zeger, S. L., Samet, J. M., & Bell, M. L. (2007) · Environmental Health Perspectives · doi:10.1289/ehp.10737 · Cited by 105 · see citing works
Are the acute effects of particulate matter on mortality in the National Morbidity, Mortality, and Air Pollution Study the result of inadequate control for weather and season? A sensitivity analysis using flexible distributed lag models
Welty, L. J., & Zeger, S. L. (2005) · American Journal of Epidemiology · doi:10.1093/aje/kwi157 · Cited by 105 · see citing works
Adverse Health Effects of Particulate Air Pollution
Bell, M. L., Ebisu, K., Peng, R. D., & Dominici, F. (2009) · Epidemiology · doi:10.1097/ede.0b013e3181aba749 · Cited by 103 · see citing works
Seasonal and temperature modifications of the association between fine particulate air pollution and cardiovascular hospitalization in New York state
Hsu, W., Hwang, S., Kinney, P. L., & Lin, S. (2016) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2016.11.008 · Cited by 95 · see citing works
Reassessing the relationship between ozone and short-term mortality in U.S. urban communities
Smith, R. L., Xu, B., & Switzer, P. (2009) · Inhalation Toxicology · doi:10.1080/08958370903161612 · Cited by 88 · see citing works
Diurnal temperature range and short-term mortality in large US communities
Lim, Y., Reid, C. E., Mann, J. K., Jerrett, M., & Kim, H. (2014) · International Journal of Biometeorology · doi:10.1007/s00484-014-0941-2 · Cited by 88 · see citing works
Impact of climate change on ambient ozone level and mortality in southeastern United States
Chang, H. H., Zhou, J., & Fuentes, M. (2010) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph7072866 · Cited by 82 · see citing works
Temperature, ozone, and mortality in urban and non-urban counties in the northeastern United States
Madrigano, J., Jack, D. W., Anderson, G. B., Bell, M. L., & Kinney, P. L. (2015) · Environmental Health · doi:10.1186/1476-069x-14-3 · Cited by 82 · see citing works
Ambient Coarse Particulate Matter and Hospital Admissions in the Medicare Cohort Air Pollution Study, 1999–2010
Powell, H., Krall, J. R., Wang, Y., Bell, M. L., & Peng, R. D. (2015) · Environmental Health Perspectives · doi:10.1289/ehp.1408720 · Cited by 80 · see citing works
Estimating the acute health effects of coarse particulate matter accounting for exposure measurement error
Chang, H. H., Peng, R. D., & Dominici, F. (2011) · Biostatistics · doi:10.1093/biostatistics/kxr002 · Cited by 80 · see citing works
Airborne Fine Particles and Risk of Hospital Admissions for Understudied Populations: Effects by Urbanicity and Short-Term Cumulative Exposures in 708 U.S. Counties
Bravo, M. A., Ebisu, K., Dominici, F., Wang, Y., Peng, R. D., & Bell, M. L. (2016) · Environmental Health Perspectives · doi:10.1289/ehp257 · Cited by 71 · see citing works
The impact of heat waves on mortality in Northwest India
Nori-Sarma, A., Anderson, G. B., Rajiva, A., ShahAzhar, G., Gupta, P., Pednekar, M. S., Son, J.-Y., Peng, R. D., & Bell, M. L. (2019) · Environmental Research · doi:10.1016/j.envres.2019.108546 · Cited by 70 · see citing works
High temperatures-related elderly mortality varied greatly from year to year: important information for heat-warning systems
Guo, Y., Barnett, A. G., & Tong, S. (2012) · Scientific Reports · doi:10.1038/srep00830 · Cited by 68 · see citing works
Mortality Related to Extreme Temperature for 15 Cities in Northeast Asia
Chung, Y., Lim, Y., Honda, Y., Guo, Y. L., Hashizume, M., Bell, M. L., Chen, B., & Kim, H. (2015) · Epidemiology · doi:10.1097/ede.0000000000000229 · Cited by 64 · see citing works
Fast Low-Rank Bayesian Matrix Completion With Hierarchical Gaussian Prior Models
Yang, L., Fang, J., Duan, H., Li, H., & Zeng, B. (2018) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2018.2816575 · Cited by 62 · see citing works
Posterior propriety and admissibility of hyperpriors in normal hierarchical models
Berger, J. O., Strawderman, W. E., & Tang, D. (2005) · The Annals of Statistics · doi:10.1214/009053605000000075 · Cited by 55 · see citing works
Asian dust and daily all-cause or cause-specific mortality in western Japan
Kashima, S., Yorifuji, T., Tsuda, T., & Eboshida, A. (2012) · Occupational and Environmental Medicine · doi:10.1136/oemed-2012-100797 · Cited by 55 · see citing works
Seasonal analysis of the short-term effects of air pollution on daily mortality in Northeast Asia
Kim, S. E., Honda, Y., Hashizume, M., Kan, H., Lim, Y., Lee, H., Kim, C. T., Yi, S., & Kim, H. (2016) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2016.10.036 · Cited by 50 · see citing works
Conservative prior distributions for variance parameters in hierarchical models
Gustafson, P., Hossain, S., & MacNab, Y. C. (2006) · Canadian Journal of Statistics · doi:10.1002/cjs.5550340302 · Cited by 49 · see citing works
Shrinkage Estimation in Multilevel Normal Models
Morris, C. N., & Lysy, M. (2012) · Statistical Science · doi:10.1214/11-sts363 · Cited by 46 · see citing works
Self-citation
Ozone and childhood respiratory disease in three US cities: evaluation of effect measure modification by neighborhood socioeconomic status using a Bayesian hierarchical approach
O’Lenick, C. R., Chang, H. H., Kramer, M. R., Winquist, A. G., Mulholland, J. A., Friberg, M. D., & Sarnat, S. E. (2017) · Environmental Health · doi:10.1186/s12940-017-0244-2 · Cited by 46 · see citing works
A Bayesian Hierarchical Distributed Lag Model for Estimating the Time Course of Risk of Hospitalization Associated with Particulate Matter Air Pollution
Peng, R. D., Dominici, F., & Welty, L. J. (2008) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/j.1467-9876.2008.00640.x · Cited by 31 · see citing works
Structural Equation Modeling
(2006) · Statistics, a series of textbooks and monographs · doi:10.1201/b15891-14 · Cited by 31 · see citing works
Temperature-mortality relationship in North Carolina, USA: Regional and urban-rural differences
Choi, H. M., Chen, C., Son, J.-Y., & Bell, M. L. (2021) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2021.147672 · Cited by 28 · see citing works
The effect of primary organic particles on emergency hospital admissions among the elderly in 3 US cities
Kioumourtzoglou, M., Zanobetti, A., Schwartz, J. D., Coull, B. A., Dominici, F., & Suh, H. H. (2013) · Environmental Health · doi:10.1186/1476-069x-12-68 · Cited by 27 · see citing works
A multicity study of air pollution and cardiorespiratory emergency department visits: Comparing approaches for combining estimates across cities
Krall, J. R., Chang, H. H., Waller, L. A., Mulholland, J. A., Winquist, A. G., Talbott, E. O., Rager, J. R., Tolbert, P. E., & Sarnat, S. E. (2018) · Environment International · doi:10.1016/j.envint.2018.07.033 · Cited by 26 · see citing works
Applying a moving total mortality count to the cities in the NMMAPS database to estimate the mortality effects of particulate matter air pollution
Roberts, S., & Martin, M. A. (2006) · Occupational and Environmental Medicine · doi:10.1136/oem.2005.023317 · Cited by 25 · see citing works
Hierarchical bivariate time series models: a combined analysis of the effects of particulate matter on morbidity and mortality
Dominici, F. (2004) · Biostatistics · doi:10.1093/biostatistics/5.3.341 · Cited by 25 · see citing works
Air quality and acute deaths in California, 2000–2012
Young, S. S., Smith, R. L., & Lopiano, K. K. (2017) · Regulatory Toxicology and Pharmacology · doi:10.1016/j.yrtph.2017.06.003 · Cited by 27 · see citing works
Associations of Particulate Matter With Stroke Mortality
Yorifuji, T., & Kashima, S. (2013) · Journal of Occupational and Environmental Medicine · doi:10.1097/jom.0b013e3182973092 · Cited by 23 · see citing works
Classifying heatwaves: developing health-based models to predict high-mortality versus moderate United States heatwaves
Anderson, G. B., Oleson, K. W., Jones, B., & Peng, R. D. (2016) · Climatic Change · doi:10.1007/s10584-016-1776-0 · Cited by 23 · see citing works
Do temporal trends of associations between short-term exposure to fine particulate matter (PM2.5) and risk of hospitalizations differ by sub-populations and urbanicity—a study of 968 U.S. counties and the Medicare population
Chen, C., Chan, A. Y., Dominici, F., Peng, R. D., Sabath, M. B., Di, Q., Schwartz, J. D., & Bell, M. L. (2021) · Environmental Research · doi:10.1016/j.envres.2021.112271 · Cited by 21 · see citing works
Distributed Reproducible Research Using Cached Computations
Peng, R. D., & Eckel, S. P. (2008) · Computing in Science & Engineering · doi:10.1109/mcse.2009.6 · Cited by 22 · see citing works
The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA?
Ritov, Y., Bickel, P. J., Gamst, A. C., & Kleijn, B. (2014) · Statistical Science · doi:10.1214/14-sts483 · Cited by 18 · see citing works
A Bayesian Algorithm for Functional Mapping of Dynamic Complex Traits
Liu, T., & Wu, R. (2009) · Algorithms · doi:10.3390/a2020667 · Cited by 16 · see citing works
Caching and Distributing Statistical Analyses inR
Peng, R. D. (2008) · Journal of Statistical Software · doi:10.18637/jss.v026.i07 · Cited by 16 · see citing works
The choice of prior distribution for a covariance matrix in multivariate meta‐analysis: a simulation study
Rúa, S. M. H., Mazumdar, M., & Strawderman, R. L. (2015) · Statistics in Medicine · doi:10.1002/sim.6631 · Cited by 15 · see citing works
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 · see citing works
Low-Rank Phase Retrieval via Variational Bayesian Learning
Liu, K., Wang, J., Xing, Z., Yang, L., & Fang, J. (2018) · IEEE Access · doi:10.1109/access.2018.2889518 · Cited by 12 · see citing works
Simulation from Wishart Distributions with Eigenvalue Constraints
Everson, P. J., & Morris, C. N. (2000) · Journal of Computational and Graphical Statistics · doi:10.2307/1390660 · Cited by 11 · see citing works
Self-citation
The effects of ambient temperature variation on respiratory hospitalizations in summer, New York State
Lin, S., Insaf, T. Z., Luo, M., & Hwang, S. (2012) · International Journal of Occupational and Environmental Health · doi:10.1179/1077352512z.00000000028 · Cited by 10 · see citing works
Methods for Bias Reduction in Time-Series Studies of Particulate Matter Air Pollution and Mortality
Roberts, S., & Martin, M. A. (2007) · Journal of Toxicology and Environmental Health · doi:10.1080/15287390600974668 · Cited by 9 · see citing works
On automating Markov chain Monte Carlo for a class of spatial modelsPreprint
Haran, M., & Tierney, L. (2012) · arXiv (Cornell University) · doi:10.48550/arxiv.1205.0499 · Cited by 9 · see citing works
Issues In Semi-Parametric Regression With Applications In Time Series Models For Air Pollution And Mortality
Dominici, F., McDermott, A., & Hastie, T. J. (2003) · Cited by 8 · see citing works
A hierarchical modeling approach to estimate regional acute health effects of particulate matter sources
Krall, J. R., Hackstadt, A. J., & Peng, R. D. (2017) · Statistics in Medicine · doi:10.1002/sim.7210 · Cited by 8 · see citing works
A class of shrinkage priors for the dependence structure in longitudinal data
Daniels, M. J. (2003) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2003.09.026 · Cited by 8 · see citing works
A Heterogeneous Clustering Approach for Human Activity Recognition
Kafle, S., & Dou, D. (2016) · Lecture notes in computer science · doi:10.1007/978-3-319-43946-4_5 · Cited by 7 · see citing works
The National Morbidity, Mortality, and Air Pollution Study Database in R
Peng, R. D., Welty, L. J., & McDermott, A. (2004) · Collection of Biostatistics Research Archive (COBRA) · Cited by 7 · see citing works
A NOTE ON FIRST-STAGE APPROXIMATION IN TWO-STAGE HIERARCHICAL MODELS*
Daniels, M. J., & Kass, R. E. (2016) · Cited by 7 · see citing works
Posterior Propriety for Hierarchical Models with Log-Likelihoods That Have Norm Bounds
Michalak, S., & Morris, C. N. (2015) · Bayesian Analysis · doi:10.1214/15-ba962 · Cited by 6 · see citing works
Self-citation
LEARNING FROM NEAR MISSES IN MEDICATION ERRORS: A BAYESIAN APPROACH
Myers, J. A., Dominici, F., & Morlock, L. (2008) · Collection of Biostatistics Research Archive · Cited by 6 · see citing works
Hierarchical Bayesian Approach to a Multi-Site Hidden Markov Model
Kim, D. H., Goh, G., & Kim, Y. (2013) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2012.732171 · Cited by 6 · see citing works
An objective prior for hyperparameters in normal hierarchical models
Berger, J. O., Sun, D., & Song, C. (2020) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2020.104606 · Cited by 5 · see citing works
The temporal trend and disparity in short-term health impacts of fine particulate matter in California (2006–2019)
Chen, C., Teyton, A., & Benmarhnia, T. (2024) · The Science of The Total Environment · doi:10.1016/j.scitotenv.2024.176543 · Cited by 4 · see citing works
A statistical inference for concentrations of benzo[a]pyrene partially measured in the ambient air of an industrial city in Korea
Kim, Y., Seo, Y.-K., & Baek, S. (2013) · Atmospheric Environment · doi:10.1016/j.atmosenv.2013.08.056 · Cited by 4 · see citing works
Variation in New Zealand hospital outcomes: combining hierarchical Bayesian modeling and propensity score methods for hospital performance comparisons
Graham, P. J., Hider, P. N., Cumming, J., Raymont, A., & Finlayson, M. (2012) · Health Services and Outcomes Research Methodology · doi:10.1007/s10742-012-0079-9 · Cited by 3 · see citing works
Frequency coverage properties of a uniform shrinkage prior distribution
Tak, H. (2017) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2017.1349769 · Cited by 3 · see citing works
Data transforming augmentation for heteroscedastic models
Tak, H., You, K., Ghosh, S. K., Su, B., & Kelly, J. (2019) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2019.1704295 · Cited by 3 · see citing works
Air quality and acute deaths in California, 2000-2012Preprint
Lopiano, K. K., Smith, R. L., & Young, S. S. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1502.03062 · Cited by 3 · see citing works
Exact bayesian inference for normal hierarchical models
Everson, P. J. (2001) · Journal of Statistical Computation and Simulation · doi:10.1080/00949650108812068 · Cited by 2 · see citing works
Self-citation
Nonparametric Bayesian analysis for multi-site hidden Markov model
Kim, D. H., Jo, A., & Kim, Y. (2016) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610918.2015.1137592 · Cited by 2 · see citing works
Conjugate distributions in hierarchical Bayesian ANOVA for computational efficiency and assessments of both practical and statistical significancePreprint
Geinitz, S., & Furrer, R. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1303.3390 · Cited by 2 · see citing works
Fast and Exact Simulation of Multivariate Normal and Wishart Random Variables with Box ConstraintsPreprint
Koch, H., & Bopp, G. P. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1907.00057 · Cited by 2 · see citing works
Posterior propriety of an objective prior for generalized hierarchical normal linear models
Lin, C., Sun, D., & Song, C. (2022) · Statistical Theory and Related Fields · doi:10.1080/24754269.2021.1978206 · Cited by 1 · see citing works
COVARIANCE MATRICES AND SKEWNESS: MODELING AND APPLICATIONS IN FINANCE
Liechty, M. W. (2003) · Cited by 1 · see citing works
An analysis of the potential impact of various ozone regulatory standards on mortality
Kim, Y. (2011) · Journal of the Korean Data and Information Science Society
Meta‐analysis and multilevel models
Congdon, P. D. (2014) · Wiley series in probability and statistics · doi:10.1002/9781118895047.ch5
Air Pollution Risk
Smith, R. L. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat03779
Estimating the effects of ambient temperature on mortality : methodological challenges and proposed solutions
Guo, Y. (2012)
BAYES AND EMPIRICAL BAYES BENCHMARKING FOR SMALL AREA ESTIM ATION
Steorts, R. C. (2012)
Statistical estimation and changepoint detection methods in public health surveillance
Reynolds, S. B. (2015) · SMARTech Repository (Georgia Institute of Technology)

Authors: Everson, P. J., & Morris, C. N.
Affiliations: Swarthmore College (US)
Harvard University (US)
Corresponding author: Everson, Philip J.
Venue: Journal of the Royal Statistical Society Series B: Statistical Methodology
Publisher: Oxford University Press (OUP)
Published: 2000-07-01
Volume: 62
Issue: 2
Pages: 399-412
ISSN: 1369-7412 (ISSN-L)
1467-9868
DOI: 10.1111/1467-9868.00239
OpenAlex: W1992951219
Cited by: 107
References: 28
Citations by year: 2025: 1 · 2024: 1 · 2022: 1 · 2021: 3 · 2020: 1 · 2019: 4 · 2018: 3 · 2017: 5 · 2016: 7 · 2015: 7 · 2014: 6 · 2013: 9 · 2012: 11
FWCI: 3.99
Type: journal article
Language: en
Open access: closed
Licence: academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
Locations: Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
Works - Scholarship, Research, & Creative Expression (Swarthmore College) (submittedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Funders: Harvard University
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
Keywords: two-level model, marginal posterior distributions, rejection sampling, empirical Bayes, posterior mean estimation, operating characteristics

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

Inference for Multivariate Normal Hierarchical Models

Abstract

Integrity signals

Claims the paper makes

Self-check

Cites

Cited by

Related

Record

About these checks