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Volumn 31, Issue 11-12, 2012, Pages 1221-1237

Hierarchical Bayesian formulations for selecting variables in regression models

Author keywords

Bayesian regularization; MC 3; Probit regression; Spike and slab; Weibull regression

Indexed keywords

ACCURACY; ACUTE GRANULOCYTIC LEUKEMIA; ARTICLE; BAYES THEOREM; COMPUTER PROGRAM; HUMAN; MEASUREMENT ERROR; METHODOLOGY; OVERALL SURVIVAL; PREDICTION; PROGNOSIS; REGRESSION ANALYSIS; RHEUMATOID ARTHRITIS; SIMULATION; SPIKE; STATISTICAL MODEL;

EID: 84861193919     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.4439     Document Type: Article
Times cited : (23)

References (65)
  • 2
    • 0030344230 scopus 로고    scopus 로고
    • Heuristics of instability and stabilization in model selection
    • Breiman L. Heuristics of instability and stabilization in model selection. The Annals of Statistics 1996; 24(6):2350-2383.
    • (1996) The Annals of Statistics , vol.24 , Issue.6 , pp. 2350-2383
    • Breiman, L.1
  • 3
    • 1542784498 scopus 로고    scopus 로고
    • Variable selection via nonconcave penalized likelihood and its oracle properties
    • Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 2001; 96:1348-1360.
    • (2001) Journal of the American Statistical Association , vol.96 , pp. 1348-1360
    • Fan, J.1    Li, R.2
  • 4
    • 0017280570 scopus 로고
    • The analysis and selection of variables in linear regression
    • Hocking R. The analysis and selection of variables in linear regression. The Annals of Statistics 1976; 32(1):1-49.
    • (1976) The Annals of Statistics , vol.32 , Issue.1 , pp. 1-49
    • Hocking, R.1
  • 9
    • 84942484786 scopus 로고
    • Ridge regression: biased estimation for nonorthogonal problems
    • Hoerl AE, Kennard RW. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 1970; 12(1):55-67.
    • (1970) Technometrics , vol.12 , Issue.1 , pp. 55-67
    • Hoerl, A.E.1    Kennard, R.W.2
  • 11
    • 84952149204 scopus 로고
    • A statistical view of some chemometrics regression tools
    • Frank IE, Friedman JH.A statistical view of some chemometrics regression tools. Technometrics 1993; 35(2):109-135.
    • (1993) Technometrics , vol.35 , Issue.2 , pp. 109-135
    • Frank, I.E.1    Friedman, J.H.2
  • 12
  • 13
    • 0001729472 scopus 로고    scopus 로고
    • Calibration and empirical Bayes variable selection
    • George EI, Foster DP. Calibration and empirical Bayes variable selection. Biometrika 2000; 87:731-747.
    • (2000) Biometrika , vol.87 , pp. 731-747
    • George, E.I.1    Foster, D.P.2
  • 15
    • 0042744696 scopus 로고    scopus 로고
    • Detecting differentially expressed genes in microarrays using Bayesian model selection
    • Ishwaran H, Rao JS. Detecting differentially expressed genes in microarrays using Bayesian model selection. Journal of the American Statistical Association 2003; 98(462):438-455.
    • (2003) Journal of the American Statistical Association , vol.98 , Issue.462 , pp. 438-455
    • Ishwaran, H.1    Rao, J.S.2
  • 18
    • 0031526204 scopus 로고    scopus 로고
    • Approaches for Bayesian variable selection
    • George EI, McCulloch RE. Approaches for Bayesian variable selection. Statistica Sinica 1997; 7(2):339-373.
    • (1997) Statistica Sinica , vol.7 , Issue.2 , pp. 339-373
    • George, E.I.1    McCulloch, R.E.2
  • 22
    • 77956890234 scopus 로고
    • Monte Carlo sampling methods using Markov chains and their applications
    • Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 1970; 57(1):97-109.
    • (1970) Biometrika , vol.57 , Issue.1 , pp. 97-109
    • Hastings, W.K.1
  • 23
    • 0000120766 scopus 로고
    • Estimating the dimension of a model
    • Schwarz G. Estimating the dimension of a model. The Annals of Statistics 1978; 6(2):461-464.
    • (1978) The Annals of Statistics , vol.6 , Issue.2 , pp. 461-464
    • Schwarz, G.1
  • 25
    • 79951540621 scopus 로고    scopus 로고
    • Evolutionary stochastic search for Bayesian model exploration
    • Bottolo L, Richardson S. Evolutionary stochastic search for Bayesian model exploration. Bayesian Analysis 2010; 5(3):583-618.
    • (2010) Bayesian Analysis , vol.5 , Issue.3 , pp. 583-618
    • Bottolo, L.1    Richardson, S.2
  • 26
    • 77956889087 scopus 로고
    • Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
    • Green P. Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 1995; 82:711-732.
    • (1995) Biometrika , vol.82 , pp. 711-732
    • Green, P.1
  • 27
    • 79956298783 scopus 로고    scopus 로고
    • Shrinkage regression for multivariate inference with missing data, and an application to portfolio balancing
    • Gramacy RB, Pantaleo E. Shrinkage regression for multivariate inference with missing data, and an application to portfolio balancing. Bayesian Analysis 2010; 5:237-262.
    • (2010) Bayesian Analysis , vol.5 , pp. 237-262
    • Gramacy, R.B.1    Pantaleo, E.2
  • 30
    • 22944460748 scopus 로고    scopus 로고
    • Spike and slab variable selection: frequentist and Bayesian strategies
    • Ishwaran H, Rao JS. Spike and slab variable selection: frequentist and Bayesian strategies. The Annals of Statistics 2005; 33(2):730-773.
    • (2005) The Annals of Statistics , vol.33 , Issue.2 , pp. 730-773
    • Ishwaran, H.1    Rao, J.S.2
  • 31
    • 3543030265 scopus 로고    scopus 로고
    • Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences
    • Johnstone IM, Silverman BW. Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences. The Annals of Statistics 2004; 32:1594-1649.
    • (2004) The Annals of Statistics , vol.32 , pp. 1594-1649
    • Johnstone, I.M.1    Silverman, B.W.2
  • 35
    • 77953326052 scopus 로고    scopus 로고
    • Bayesian regularisation in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection
    • Fahrmeir L, Kneib T, Konrath S. Bayesian regularisation in structured additive regression: a unifying perspective on shrinkage, smoothing and predictor selection. Statistics and Computing 2010; 20(2):203-219.
    • (2010) Statistics and Computing , vol.20 , Issue.2 , pp. 203-219
    • Fahrmeir, L.1    Kneib, T.2    Konrath, S.3
  • 38
    • 78650337471 scopus 로고    scopus 로고
    • Inference with normal-gamma prior distributions in regression problems
    • Griffin JE, Brown PJ. Inference with normal-gamma prior distributions in regression problems. Bayesian Analysis 2010; 5:17-188.
    • (2010) Bayesian Analysis , vol.5 , pp. 17-188
    • Griffin, J.E.1    Brown, P.J.2
  • 39
    • 12344304266 scopus 로고    scopus 로고
    • Gene selection using a two-level hierarchical Bayesian model
    • Bae K, Mallick BK. Gene selection using a two-level hierarchical Bayesian model. Bioinformatics 2004; 20(18):3423-3430.
    • (2004) Bioinformatics , vol.20 , Issue.18 , pp. 3423-3430
    • Bae, K.1    Mallick, B.K.2
  • 41
    • 77952811536 scopus 로고    scopus 로고
    • The horseshoe estimator for sparse signals
    • Carvalho CM, Polson NG, Scott JG. The horseshoe estimator for sparse signals. Biometrika 2010; 97:465-480.
    • (2010) Biometrika , vol.97 , pp. 465-480
    • Carvalho, C.M.1    Polson, N.G.2    Scott, J.G.3
  • 42
    • 77953359190 scopus 로고    scopus 로고
    • Model uncertainty and variable selection in Bayesian lasso regression
    • Hans C. Model uncertainty and variable selection in Bayesian lasso regression. Statistics and Computing 2010; 20:221-229.
    • (2010) Statistics and Computing , vol.20 , pp. 221-229
    • Hans, C.1
  • 43
    • 0039713775 scopus 로고
    • On scale mixtures of normal distributions
    • West M. On scale mixtures of normal distributions. Biometrika 1987; 74(3):646-648.
    • (1987) Biometrika , vol.74 , Issue.3 , pp. 646-648
    • West, M.1
  • 44
    • 84988112810 scopus 로고
    • Inference for nonconjugate Bayesian models using the Gibbs sampler
    • Carlin BP, Polson NG. Inference for nonconjugate Bayesian models using the Gibbs sampler. The Canadian Journal of Statistics 1991; 19:399-405.
    • (1991) The Canadian Journal of Statistics , vol.19 , pp. 399-405
    • Carlin, B.P.1    Polson, N.G.2
  • 45
    • 71249130909 scopus 로고    scopus 로고
    • Bayesian lasso regression
    • Hans C. Bayesian lasso regression. Biometrika 2009; 96:835-845.
    • (2009) Biometrika , vol.96 , pp. 835-845
    • Hans, C.1
  • 47
    • 78049484065 scopus 로고    scopus 로고
    • Penalized regression, standard errors, and Bayesian lassos
    • Kyung M, Gilly J, Ghoshz M, Casella G. Penalized regression, standard errors, and Bayesian lassos. Bayesian Analysis 2010; 5(2):369-412.
    • (2010) Bayesian Analysis , vol.5 , Issue.2 , pp. 369-412
    • Kyung, M.1    Gilly, J.2    Ghoshz, M.3    Casella, G.4
  • 48
    • 79551657781 scopus 로고    scopus 로고
    • The Bayesian elastic net
    • Li Q, Lin N. The Bayesian elastic net. Bayesian Analysis 2010; 5(1):151-170.
    • (2010) Bayesian Analysis , vol.5 , Issue.1 , pp. 151-170
    • Li, Q.1    Lin, N.2
  • 50
    • 84867151416 scopus 로고    scopus 로고
    • Bayesian auxiliary variable models for binary and multinomial regression
    • Holmes CC, Held L. Bayesian auxiliary variable models for binary and multinomial regression. Bayesian Analysis 2006; 1:145-168.
    • (2006) Bayesian Analysis , vol.1 , pp. 145-168
    • Holmes, C.C.1    Held, L.2
  • 52
    • 77950497193 scopus 로고    scopus 로고
    • Bayesian variable selection for disease classification using gene expression data
    • Yang A-J, Song X-Y. Bayesian variable selection for disease classification using gene expression data. Bioinformatics 2010; 26(2):215-222.
    • (2010) Bioinformatics , vol.26 , Issue.2 , pp. 215-222
    • Yang, A.-J.1    Song, X.-Y.2
  • 53
    • 4744364173 scopus 로고    scopus 로고
    • Cancer classification and prediction using logistic regression with Bayesian gene selection
    • Zhou X, Liu KY, Wong ST. Cancer classification and prediction using logistic regression with Bayesian gene selection. Journal of Biomedical Informatics 2004; 37(4):249-259.
    • (2004) Journal of Biomedical Informatics , vol.37 , Issue.4 , pp. 249-259
    • Zhou, X.1    Liu, K.Y.2    Wong, S.T.3
  • 54
    • 33748686773 scopus 로고    scopus 로고
    • Bayesian variable selection for the analysis of microarray data with censored outcomes
    • Sha N, Tadesse MG, Vannucci M. Bayesian variable selection for the analysis of microarray data with censored outcomes. Bioinformatics 2006; 22(18):2262-2268.
    • (2006) Bioinformatics , vol.22 , Issue.18 , pp. 2262-2268
    • Sha, N.1    Tadesse, M.G.2    Vannucci, M.3
  • 55
    • 77950537175 scopus 로고    scopus 로고
    • Regularization paths for generalized linear models via coordinate descent
    • Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software 2010; 33(1):1-22.
    • (2010) Journal of Statistical Software , vol.33 , Issue.1 , pp. 1-22
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 56
    • 4544388285 scopus 로고    scopus 로고
    • Gibbs variable selection using BUGS
    • Ntzoufras I. Gibbs variable selection using BUGS. Journal of Statistical Software 2002; 7(7):1-19.
    • (2002) Journal of Statistical Software , vol.7 , Issue.7 , pp. 1-19
    • Ntzoufras, I.1
  • 57
    • 84861201794 scopus 로고    scopus 로고
    • Bayesian methods for highly correlated exposure data
    • Nott DJ. Bayesian methods for highly correlated exposure data. Epidemiology 2008; 28(3):199-207.
    • (2008) Epidemiology , vol.28 , Issue.3 , pp. 199-207
    • Nott, D.J.1
  • 58
    • 40249119787 scopus 로고    scopus 로고
    • Predictive performance of Dirichlet process shrinkage methods in linear regression
    • Nott DJ. Predictive performance of Dirichlet process shrinkage methods in linear regression. Computational Statistics & Data Analysis 2008; 52(7):3658-3669.
    • (2008) Computational Statistics & Data Analysis , vol.52 , Issue.7 , pp. 3658-3669
    • Nott, D.J.1
  • 59
    • 79956309875 scopus 로고    scopus 로고
    • Spiked Dirichlet process prior for Bayesian multiple hypothesis testing in random effects models
    • Kim S, Dahly DB, Vannucci M. Spiked Dirichlet process prior for Bayesian multiple hypothesis testing in random effects models. Bayesian Analysis 2009; 4(4):707-732.
    • (2009) Bayesian Analysis , vol.4 , Issue.4 , pp. 707-732
    • Kim, S.1    Dahly, D.B.2    Vannucci, M.3
  • 61
    • 50449094780 scopus 로고    scopus 로고
    • On optimality of Bayesian testimation in the normal means problem
    • Abramovich F, Angelini C, De Canditiis D. On optimality of Bayesian testimation in the normal means problem. Annals of Statistics 2007; 35(5):2261-2286.
    • (2007) Annals of Statistics , vol.35 , Issue.5 , pp. 2261-2286
    • Abramovich, F.1    Angelini, C.2    De Canditiis, D.3
  • 64
    • 44249109682 scopus 로고    scopus 로고
    • A general approach to simultaneous model fitting and variable elimination in response models for biological data with many more variables than observations
    • Kiiveri HT.A general approach to simultaneous model fitting and variable elimination in response models for biological data with many more variables than observations. BMC Bioinformatics 2008; 9(195):1-9.
    • (2008) BMC Bioinformatics , vol.9 , Issue.195 , pp. 1-9
    • Kiiveri, H.T.1
  • 65


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