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Review Article

On Sampling Strategies in Bayesian Variable Selection Problems With Large Model Spaces

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Pages 340-352 | Received 01 Mar 2012, Published online: 15 Mar 2013

REFERENCES

  • Barbieri , M. M. and Berger , J. O. 2004 . “Optimal Predictive Model Selection,” . The Annals of Statistics , 32 : 870 – 897 .
  • Bayarri , M. J. and García-Donato , G. 2008 . “Generalization of Jeffreys Divergence-Based Priors for Bayesian Hypothesis Testing,” . Journal of the Royal Statistical Society, Series B , 70 : 981 – 1003 .
  • Berger , J. O. and Molina , G. 2005 . “Posterior Model Probabilities via Path-Based Pairwise Priors,” . Statistica Neerlandica , 59 : 3 – 15 .
  • Berger , J. O. and Pericchi , L. R. 2001 . “Objective Bayesian Methods for Model Selection: Introduction and Comparison,” . Lecture Notes-Monograph Series , 38 : 135 – 207 .
  • Carvalho , C. and Scott , J. 2009 . “Objective Bayesian Model Selection in Gaussian Graphical Models,” . Biometrika , 96 : 497 – 512 .
  • Casella , G. and Moreno , E. 2006 . “Objective Bayesian Variable Selection,” . Journal of the American Statistical Association , 101 : 157 – 167 .
  • Chan , K. S. and Geyer , C. T. 1994 . Discussion to “Markov Chains for Exploring Posterior Distributions,” . The Annals of Statistics , 22 : 1747 – 1758 .
  • Chib , S. and Jeliazkov , I. 2001 . “Marginal Likelihood From the Metropolis-Hastings Output,” . Journal of the American Statistical Association , 96 : 270 – 281 .
  • Clyde , M. A. , DeSimone , H. and Parmigiani , G. 1996 . “Prediction via Orthogonalized Model Mixing,” . Journal of the American Statistical Association , 91 : 1197 – 1208 .
  • Clyde , M. A. and George , E. I. 2004 . “Model Uncertainty,” . Statistical Science , 19 : 81 – 94 .
  • Clyde , M. A. and Ghosh , J. 2012 . “Finite Population Estimators in Stochastic Search Variable Selection,” . Technical report 2010-11, Department of Statistics of Duke University. Available at http://stat.duke.edu/research/papers/2010-11
  • Clyde , M. A. , Ghosh , J. and Littman , M. L. 2011 . “Bayesian Adaptive Sampling for Variable Selection and Model Averaging,” . Journal of Computational and Graphical Statistics , 20 : 80 – 101 .
  • Dellaportas , P. , Forster , J. and Ntzoufras , I. 2000 . “Bayesian Variable Selection Using the Gibbs Sampler,” . In Generalized Linear Models: A Bayesian Perspective Edited by: Dey , D. , Ghosh , S. K. and Mallick , B. K. New York-Basel: Marcel Dekker, Inc.
  • Forte , A. 2011 . “Objective Bayes Criteria for Variable Selection,” . Ph.D. dissertation, Department of Statistics at the University of Valencia
  • Galassi , M. , Davies , J. , Theiler , J. , Gough , B. , Jungman , G. , Alken , P. , Booth , M. and Rossi , F. 2009 . GNU Scientific Library Reference Manual (v1.12, 3rd ed.) , United Kingdom: Network Theory Ltd .
  • George , E. I. and McCulloch , R. E. 1993 . “Variable Selection via Gibbs Sampling,” . Journal of the American Statistical Association , 88 : 881 – 889 .
  • George , E. I. and McCulloch , R. E. 1997 . “Approaches for Bayesian Variable Selection,” . Statistica Sinica , 7 : 339 – 373 .
  • Geyer , C. J. 1992 . “Practical Markov Chain Monte Carlo,” . Statistical Science , 7 : 473 – 511 .
  • Hans , C. , Dobra , A. and West , M. 2007 . “Shotgun Stochastic Search for Regression With Many Candidate Predictors,” . Journal of the American Statistical Association , 102 : 507 – 516 .
  • Hansen , M. H. and Hurwitz , W. N. 1943 . “The Theory of Sampling From Finite Populations,” . Annals of Mathematical Statistics , 14 : 333 – 362 .
  • Heaton , M. J. and Scott , J. G. 2010 . “Bayesian Computation and the Linear Model,” . In Frontiers of Statistical Decision Making and Bayesian Analysis , Edited by: Chen , M.-H. , Mller , P. , Sun , D. , Ye , K. and Dey , D. K. 527 – 544 . New York : Springer .
  • Hoeting , J. A. , Madigan , D. , Raftery , A. E. and Volinsky , C. T. 1999 . “Bayesian Model Averaging: A Tutorial,” . Statistical Science , 14 : 382 – 401 .
  • Jeffreys , H. 1961 . Theory of Probability (3rd ed.) , Oxford : Oxford University Press .
  • Kuo , L. and Mallick , B. 1998 . “Variable Selection for Regression Models,” . Sankhya: The Indian Journal of Statistics , 60 : 65 – 81 .
  • Ley , E. and Steel , M. F. J. 2007 . “Jointness in Bayesian Variable Selection with Applications to Growth Regression,” . Journal of Macroeconomics , 29 : 476 – 493 .
  • Liang , F. , Paulo , R. , Molina , G. , Clyde , M. A. and Berger , J. O. 2008 . “Mixtures of g Priors for Bayesian Variable Selection,” . Journal of the American Statistical Association , 103 : 410 – 423 .
  • Lohr , S. L. 1999 . Sampling: Design and Analysis , Pacific Grove , CA : Duxbury Press .
  • Madigan , D. and Raftery , A. E. 1994 . “Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam’s Window,” . Journal of the American Statistical Association , 89 : 1535 – 1546 .
  • Madigan , D. and York , J. 1995 . “Bayesian Graphical Models for Discrete Data,” . International Statistical Review , 63 : 215 – 232 .
  • Maruyama , Y. and George , E. I. 2011 . “Fully Bayes Factors With a Generalized g-prior,” . The Annals of Statistics , 39 : 2740 – 2765 .
  • Nott , D. and Kohn , R. 2005 . “Adaptive Sampling for Bayesian Variable Selection,” . Biometrika , 92 : 747 – 762 .
  • Ntzoufras , I. 2002 . “Gibbs Variable Selection Using BUGS,” . Journal of Statistical Software , 7 : 1 – 19 .
  • Ntzoufras , I. 2009 . Bayesian Modeling Using WinBUGS: Wiley Series in Computational Statistics , New York : Wiley .
  • Raftery , A. E. 1998 . “Bayes Factors and BIC: Comment on Weakliem,” . Technical Report 347, Department of Statistics, University of Washington
  • Raftery , A. E. , Madigan , D. and Hoeting , J. 1997 . “Bayesian Model Averaging for Linear Regression Models,” . Journal of the American Statistical Association , 92 : 179 – 191 .
  • Royall , R. M. 1970 . “On Finite Population Sampling Theory Under Certain Linear Regression Models,” . Biometrika , 57 : 377 – 387 .
  • Scott , J. and Carvalho , C. 2009 . “Feature-Inclusion Stochastic Search for Gaussian Graphical Models,” . Journal of Computational and Graphical Statistics , 17 : 790 – 808 .
  • Thompson , S. K. 2002 . Sampling (2nd ed.) , New York : Wiley .
  • Tierney , L. 1994 . “Markov Chains for Exploring Posterior Distributions,” (with discussion and a rejoinder by the author) . The Annals of Statistics , 22 : 1701 – 1762 .
  • Zellner , A. (ed.) . 1986 . “On Assessing Prior Distributions and Bayesian Regression Analysis With g-prior Distributions,” . In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti , 389 – 399 . North Holland: Edward Elgar Publishing Limited .
  • Zellner , A. and Siow , A. 1980 . “Posterior Odds Ratio for Selected Regression Hypotheses,” . In Bayesian Statistics 1 , Edited by: Bernardo , J. M. , DeGroot , M. H. , Lindley , D. V. and Smith , Adrian F. M. Valencia : University Press, pp. 585–603 .
  • Zellner , A. and Siow , A. 1984 . Basic Issues in Econometrics , Chicago : University of Chicago Press .

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