Bayesian Analysis: A Look at Today and Thoughts of Tomorrow

References

• Albert , J. H. 1996 . Bayesian Computation Using Minitab , Belmont , CA : Wadsworth .
   Google Scholar
• Andrews , R. , Berger , J. and Smith , M. 1993 . “Bayesian Estimation of Fuel Economy Potential due to Technology Improvements,” . In Case Studies in Bayesian Statistics , Edited by: Gatsonis , C. 1 – 77 . New York : Springer-Verlag .
   Google Scholar
• Antleman , G. 1997 . Elementary Bayesian Statistics , Hong Kong : Edward Elgar .
   Google Scholar
• Aitchison , J. and Dunsmore , I. R. 1975 . Statistical Prediction Analysis , New York : Wiley .
   Google Scholar
• Barron , A. , Rissanen , J. and Yu , B. 1998 . “The Minimum Description Length Principle in Coding and Modeling” . IEEE Transactions on Information Theory , 44 : 2743 – 2760 .
   Web of Science ®Google Scholar
• Bayes , T. 1783 . “An Essay Towards Solving a Problem in the Doctrine of Chances” . Philosophical Transactions of the Royal Society , 53 : 370 – 418 .
   Google Scholar
• Bayarri , M. J. and Berger , J. 2000 . “P-Values for Composite Null Models” . Journal of the American Statistical Association , 95 : 1127 – 1142 .
   Web of Science ®Google Scholar
• Berger , J. 1985 . Statistical Decision Theory and Bayesian Analysis, , 2nd ed. , New York : Springer-Verlag .
   Google Scholar
• Berger , J. 1994 . “An Overview of Robust Bayesian Analysis” . Test , 3 : 5 – 124 .
   Google Scholar
• Berger , J. 1998 . “Bayes Factors,” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. Volume 3 , New York : Wiley . (update)
   Google Scholar
• Berger , J. and Berry , D. 1988 . “Analyzing Data: Is Objectivity Possible?” . The American Scientist , 76 : 159 – 165 .
   Web of Science ®Google Scholar
• Berger , J. , Betró , B. , Moreno , E. , Pericchi , L. R. , Ruggeri , F. , Salinetti , G. and Wasserman , L. 1996 . Bayesian Robustness , Hayward , CA : Institute of Mathematical Statistics .
   Google Scholar
• Berger , J. , Boukai , B. and Wang , W. 1997 . “Unified Frequentist and Bayesian Testing of Precise Hypotheses” . Statistical Science , 12 : 133 – 160 .
   Web of Science ®Google Scholar
• Berger , J. and Pericchi , L. R. 1996 . “The Intrinsic Bayes Factor for Model Selection and Prediction” . Journal of the American Statistical Association , 91 : 109 – 122 .
   Web of Science ®Google Scholar
• Berliner , L. M. , Royle , J. A. , Wikle , C. K. and Milliff , R. F. 1999 . “Bayesian Methods in the Atmospheric Sciences,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 83 – 100 . London : Oxford University Press .
   Google Scholar
• Bernardo , J. M. 1979 . “Reference Posterior Distributions for Bayesian Inference” (with discussion)” . Journal of the Royal Statistical Society , 41 : 113 – 147 . Ser. B
   Google Scholar
• Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 1999 . Bayesian Statistics 6 , London : Oxford University Press .
   Google Scholar
• Bernardo , J. M. and Smith , A. F. M. 1994 . Bayesian Theory , New York : Wiley .
   Google Scholar
• Berry , D. A. 1996 . Statistics: A Bayesian Perspective , Belmont , CA : Wadsworth .
   Google Scholar
• Berry , D. A. and Stangl , D. K. 1996 . Bayesian Biostatistics , New York : Marcel Dekker .
   Google Scholar
• Berry , D. A. and Stangl , D. K. 2000 . Meta-Analysis in Medicine and Health Policy , New York : Marcel Dekker .
   Google Scholar
• Besag , J. and Higdon , D. 1999 . “Bayesian Inference for Agricultural Field Experiments” . Journal of the Royal Statistical Society , 61 : 691 – 746 . (with Discussion), Ser. B
   Google Scholar
• Bolfarine , H. and Zacks , S. 1992 . Prediction Theory for Finite Populations , New York : Springer-Verlag .
   Google Scholar
• Box , G. and Tiao , G. 1973 . Bayesian Inference in Statistical Analysis , Reading , MA : Addison-Wesley .
   Google Scholar
• Bretthorst , G. L. 1988 . Bayesian Spectrum Analysis and Parameter Estimation , New York : Springer-Verlag .
   Google Scholar
• Broemeling , L. D. 1985 . Bayesian Analysis of Linear Models , New York : Marcel Dekker .
   Google Scholar
• Brown , P. J. 1993 . Measurement, Regression, and Calibration , Oxford , , U.K. : Clarendon Press .
   Google Scholar
• Buck , C. E. , Cavanagh , W. G. and Litton , C. D. 1996 . The Bayesian Approach to Interpreting Archaeological Data , New York : Wiley .
   Google Scholar
• Carlin , B. P. and Louis , T. A. 1996 . Bayes and Empirical Bayes Methods for Data Analysis , London : Chapman and Hall .
   Google Scholar
• Carlin , B. , Kadane , J. and Gelfand , A. 1998 . “Approaches for Optimal Sequential Decision Analysis in Clinical Trials” . Biometrics , 54 : 964 – 975 .
   PubMed Web of Science ®Google Scholar
• Chaloner , K. and Verdinelli , I. 1995 . “Bayesian Experimental Design: A Review” . Statistical Science , 10 : 273 – 304 .
   Web of Science ®Google Scholar
• Chen , M. H. , Shao , Q. M. and Ibrahim , J. G. 2000 . Monte Carlo Methods in Bayesian Computation , New York : Springer-Verlag .
   Google Scholar
• Clarotti , C. A. , Barlow , R. E. and Spizzichino , F. 1993 . Reliability and Decision Making , Amsterdam : Elsevier Science .
   Google Scholar
• Clemen , R. T. 1996 . Making Hard Decisions: An Introduction to Decision Analysis, , 2nd ed. , Belmont , CA : Duxbury .
   Google Scholar
• Clyde , M. A. 1999 . “Bayesian Model Averaging and Model Search Strategies,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 23 – 42 . London : Oxford University Press .
   Google Scholar
• Cowell , R. G. , Dawid , A. P. , Lauritzen , S. L. and Spiegelhalter , D. J. 1999 . Probabilistic Networks and Expert Systems , New York : Springer .
   Google Scholar
• Cyert , R. M. and DeGroot , M. H. 1987 . Bayesian Analysis in Economic Theory , Totona , NJ : Rowman Littlefield .
   Google Scholar
• Dale , A. I. 1991 . A History of Inverse Probability , New York : Springer-Verlag .
   Google Scholar
• Dawid , A. P. and Pueschel , J. 1999 . “Hierarchical Models for DNA Profiling Using Heterogeneous Databases,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 187 – 212 . London : Oxford University Press .
   Google Scholar
• de Finetti , B. 1974, 1975 . Theory of Probability , Vols. 1 and 2 , New York : Wiley .
   Google Scholar
• DeGroot , M. H. 1970 . Optimal Statistical Decisions , New York : McGraw-Hill .
   Google Scholar
• DeGroot , M. H. , Fienberg , S. E. and Kadane , J. B. 1986 . Statistics and the Law , New York : Wiley .
   Google Scholar
• Dey , D. , Ghosh , S. and Mallick , B. K. 2000 . Bayesian Generalized Linear Models , New York : Marcel Dekker .
   Google Scholar
• Dey , D. , Müller , P. and Sinha , D. 1998 . Practical Nonparametric and Semiparametric Bayesian Statistics , New York : Springer-Verlag .
   Google Scholar
• Diaconis , P. and Freedman , D. 1986 . “On the Consistency of Bayes Estimates” . The Annals of Statistics , 14 : 1 – 67 .
   Web of Science ®Google Scholar
• Draper , D. 1995 . “Assessment and Propagation of Model Uncertainty” . Journal of the Royal Statistical Society , 57 : 45 – 98 . Ser. B
   Google Scholar
• Erickson , G. , Rychert , J. and Smith , C. R. 1998 . Maximum Entropy and Bayesian Methods , Norwell , MA : Kluwer Academic .
   Google Scholar
• Fitzgerald , W. J. , Godsill , S. J. , Kokaram , A. C. and Stark , J. A. 1999 . “Bayesian Methods in Signal and Image Processing,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 239 – 254 . London : Oxford University Press .
   Google Scholar
• Florens , J. P. , Mouchart , M. and Roulin , J. M. 1990 . Elements of Bayesian Statistics , New York : Marcel Dekker .
   Google Scholar
• French , S. and Smith , J. Q. 1997 . The Practice of Bayesian Analysis , London : Arnold .
   Google Scholar
• Gamerman , D. 1997 . Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference , London : Chapman and Hall .
   Google Scholar
• Gatsonis , C. , Kass , R. , Carlin , B. P. , Carriquiry , A. L. , Gelman , A. , Verdinelli , I. and West , M. 1998 . Case Studies in Bayesian Statistics IV , New York : Springer-Verlag .
   Google Scholar
• Geisser , S. 1993 . Predictive Inference: An Introduction , London : Chapman and Hall .
   Google Scholar
• Gelman , A. , Carlin , J. B. , Stern , H. S. and Rubin , D. B. 1995 . Bayesian Data Analysis , London : Chapman and Hall .
   Google Scholar
• Geweke , J. 1999 . “Using Simulation Methods for Bayesian Econometric Models: Inference, Development and Communication” . Econometric Reviews , 18 : 1 – 73 . (with discussion)
   Google Scholar
• Glymour , C. and Cooper , G. 1999 . Computation, Causation, and Discovery , Cambridge , MA : MIT Press .
   Google Scholar
• Godsill , S. J. and Rayner , P. J. W. 1998 . Digital Audio Restoration , Berlin : Springer .
   Google Scholar
• Goel , P. 1988 . “Software for Bayesian Analysis: Current Status and Additional Needs,” . In Bayesian Statistics 3 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. London : Oxford University Press .
   Google Scholar
• Goldstein , M. 1998 . “Bayes Linear Analysis,” . In Encyclopedia of Statistical Sciences, Update , Vol. 3 , New York : Wiley .
   Google Scholar
• Good , I. J. 1983 . Good Thinking: The Foundations of Probability and Its Applications , Minneapolis : University of Minnesota Press .
   Google Scholar
• Greenland , S. 1998 . “Probability Logic and Probability Induction” . Epidemiology , 9 : 322 – 332 .
   PubMed Web of Science ®Google Scholar
• Hartigan , J. A. 1983 . Bayes Theory , New York : Springer-Verlag .
   Google Scholar
• Howson , C. and Urbach , P. 1990 . Scientific Reasoning: The Bayesian Approach , La Salle , IL : Open Court .
   Google Scholar
• Iversen , E. Jr. , Parmigiani , G. and Berry , D. 1998 . “Validating Bayesian Prediction Models: A Case Study in Genetic Susceptibility to Breast Cancer,” . In Case Studies in Bayesian Statistics IV , Edited by: Gatsonis , C. , Kass , R. E. , Carlin , B. , Carriquiry , A. , Gelman , A. , Verdinelli , I. and West , M. New York : Springer-Verlag .
   Google Scholar
• Jaynes , E. T. 1999 . “Probability Theory: The Logic of Science,” accessible at http://bayes.wustl.edu/etj/prob.html
   Google Scholar
• Jeffreys , H. 1961 . Theory of Probability, , 3rd ed. , London : Oxford University Press .
   Google Scholar
• Jensen , F. V. 1996 . An Introduction to Bayesian Networks , London : University College of London Press .
   Google Scholar
• Johnson , V. E. 1997 . “An Alternative to Traditional GPA for Evaluating Student Performance” . Statistical Science , 12 : 251 – 278 .
   Web of Science ®Google Scholar
• Johnson , V. E. and Albert , J. 1999 . Ordinal Data Models , New York : Springer-Verlag .
   Google Scholar
• Jordan , M. I. 1998 . Learning in Graphical Models , Cambridge , MA : MIT Press .
   Google Scholar
• Kadane , J. 1984 . Robustness of Bayesian Analysis , Amsterdam : North-Holland .
   Google Scholar
• Kadane , J. 1996 . Bayesian Methods and Ethics in a Clinical Trial Design , New York : Wiley .
   Google Scholar
• Kadane , J. , Schervish , M. and Seidenfeld , T. 1999 . Rethinking the Foundations of Statistics , Cambridge , , U.K. : Cambridge University Press .
   Google Scholar
• Kadane , J. and Schuan , D. A. 1996 . A Probabilistic Analysis of the Sacco and Vanzetti Evidence , New York : Wiley .
   Google Scholar
• Kahneman , D. , Slovic , P. and Tversky , A. 1986 . Judgment Under Uncertainty: Heuristics and Biases , Cambridge , , U.K. : Cambridge University Press .
   Google Scholar
• Kass , R. and Raftery , A. 1995 . “Bayes Factors and Model Uncertainty” . Journal of the American Statistical Association , 90 : 773 – 795 .
   Web of Science ®Google Scholar
• Kass , R. and Wasserman , L. 1996 . “The Selection of Prior Distributions by Formal Rules” . Journal of the American Statistical Association , 91 : 1343 – 1370 .
   Web of Science ®Google Scholar
• Kim , S. , Shephard , N. and Chib , S. 1998 . “Stochastic Volatility: Likelihood Inference and Comparison With ARCH Models” . Review of Economic Studies , 65 : 361 – 194 .
   Web of Science ®Google Scholar
• Kitagawa , G. and Gersch , W. 1996 . Smoothness Priors Analysis of Time Series , New York : Springer .
   Google Scholar
• Lad , F. 1996 . Operational Subjective Statistical Methods , New York : Wiley .
   Google Scholar
• Lauritzen , S. L. 1996 . Graphical Models , London : Oxford University Press .
   Google Scholar
• Laplace , P. S. 1812 . Théorie Analytique des Probabilités , Paris : Courcier .
   Google Scholar
• Leamer , E. E. 1978 . Specification Searches: Ad Hoc Inference With Non-experimental Data , Chichester , , U.K. : Wiley .
   Google Scholar
• Lee , P. M. 1997 . Bayesian Statistics: An Introduction , London : Edward Arnold .
   Google Scholar
• Lindley , D. V. 1972 . Bayesian Statistics, A Review , Philadelphia : SIAM .
   Google Scholar
• Liseo , B. , Petrella , L. and Salinetti , G. 1996 . “Robust Bayesian Analysis: An Interactive Approach,” . In Bayesian Statistics 5 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 661 – 666 . London : Oxford University Press .
   Google Scholar
• Liu , J. , Neuwald , A. and Lawrence , C. 1999 . “Markovian Structures in Biological Sequence Alignments” . Journal of the American Statistical Association , 94 : 1 – 15 .
   Web of Science ®Google Scholar
• Lynn , N. , Singpurwalla , N. and Smith , A. 1998 . “Bayesian Assessment of Network Reliability” . SIAM Review , 40 : 202 – 227 .
   Web of Science ®Google Scholar
• Monahan , J. and Genz , A. 1996 . “A Comparison of Omnibus Methods for Bayesian Computation” . Computing Science and Statistics , 27 : 471 – 480 .
   Google Scholar
• Müller , P. M. 1999 . “Simulation-Based Optimal Design,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 459 – 474 . London : Oxford University Press .
   Google Scholar
• Müller , P. M. and Rios-Insua , D. 1998 . “Issues in Bayesian Analysis of Neural Network Models” . Neural Computation , 10 : 571 – 592 .
   Web of Science ®Google Scholar
• Müller , P. M. and Vidakovic , B. 1999 . Bayesian Inference in Wavelet-Based Models , New York : Springer-Verlag .
   Google Scholar
• Mukhopadhyay , P. 1998 . Small Area Estimation in Survey Sampling , New Delhi : Naroso .
   Google Scholar
• Neal , R. M. 1996 . Bayesian Learning for Neural Networks , New York : Springer .
   Google Scholar
• Neal , R. M. 1999 . “Regression and Classification Using Gaussian Process Priors,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 475 – 501 . London : Oxford University Press .
   Google Scholar
• O'Hagan , A. 1988 . Probability: Methods and Measurements , London : Chapman and Hall .
   Google Scholar
• O'Hagan , A. 1994 . Kendall's Advanced Theory of Statistics, Vol. 2B–Bayesian Inference , London : Arnold .
   Google Scholar
• O'Hagan , A. 1995 . “Fractional Bayes Factors for Model Comparisons” . Journal of the Royal Statistical Society , 57 : 99 – 138 . Ser. B
   Google Scholar
• Ruanaidh , J.J. K. Ó. and Fitzgerald , W. J. 1996 . Numerical Bayesian Methods Applied to Signal Processing , New York : Springer .
   Google Scholar
• Parent , E. , Hubert , P. , Bobée , B. and Miquel , J. 1998 . Statistical and Bayesian Methods in Hydrological Sciences , Paris : UNESCO Press .
   Google Scholar
• Pearl , J. 1988 . Probabilistic Inference in Intelligent Systems , San Mateo , CA : Morgan Kaufmann .
   Google Scholar
• Perlman , M. and Blaug , M. 1997 . Bayesian Analysis in Econometrics and Statistics: The Zellner View , Northhampton , MA : Edward Elgar .
   Google Scholar
• Piccinato , L. 1996 . Metodi per le Decisioni Statistiche , Milano : Springer-Verlag Italia .
   Google Scholar
• Pilz , J. 1991 . Bayesian Estimation and Experimental Design in Linear Regression, , 2nd ed. , New York : Wiley .
   Google Scholar
• Poirier , D. J. 1995 . Intermediate Statistics and Econometrics: A Comparative Approach , Cambridge , MA : MIT Press .
   Google Scholar
• Pole , A. , West , M. and Harrison , J. 1995 . Applied Bayesian Forecasting Methods , London : Chapman and Hall .
   Google Scholar
• Pollard , W. E. 1986 . Bayesian Statistics for Evaluation Research , Beverly Hills , CA : Sage .
   Google Scholar
• Press , J. 1989 . Bayesian Statistics , New York : Wiley .
   Google Scholar
• Qian , W. and Brown , P. J. 1999 . “Bayes Sequential Decision Theory in Clinical Trials,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 829 – 838 . London : Oxford University Press .
   Google Scholar
• Racugno , W. Proceedings of the Workshop on Model Selection . Bologna : Pitagora Editrice . Special issue of Rassegna di Metodi Statistici ed Applicazioni
   Google Scholar
• Regazzini , E. 1999 . “Old and Recent Results on the Relationship Between Predictive Inference and Statistical Modelling Either in Nonparametric or Parametric Form,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 571 – 588 . London : Oxford University Press .
   Google Scholar
• Insua , D. Rios . 1990 . Sensitivity Analysis in Multiobjective Decision Making , New York : Springer-Verlag .
   Google Scholar
• Robert , C. P. 1994 . The Bayesian Choice: A Decision-Theoretic Motivation , New York : Springer .
   Google Scholar
• Robert , C. P. and Casella , G. 1999 . Monte Carlo Statistical Methods , New York : Springer-Verlag .
   Google Scholar
• Rubin , D. B. 1987 . Multiple Imputation for Nonresponse in Surveys , New York : Wiley .
   Google Scholar
• Savage , L. J. 1972 . The Foundations of Statistics, , 2nd ed. , New York : Dover .
   Google Scholar
• Sellke , T. , Bayarri , M. J. and Berger , J. O. 1999 . “Calibration of P Values for Precise Null Hypotheses,” , Duke University . ISDS Discussion Paper 99–13
   Google Scholar
• Schervish , M. 1995 . Theory of Statistics , New York : Springer .
   Google Scholar
• Sinha , D. and Dey , D. 1999 . “Survival Analysis Using Semiparametric Bayesian Methods,” . In Practical Nonparametric and Semiparametric Statistics , Edited by: Dey , D. , Müller , P. and Sinha , D. 195 – 211 . New York : Springer .
   Google Scholar
• Sivia , D. S. 1996 . Data Analysis: A Bayesian Tutorial , London : Oxford University Press .
   Google Scholar
• Smith , J. Q. 1988 . Decision Analysis: A Bayesian Approach , London : Chapman and Hall .
   Google Scholar
• Spirtes , P. , Glymour , C. and Scheines , R. 1993 . Causation, Prediction, and Search , New York : Springer-Verlag .
   Google Scholar
• Stangl , D. and Berry , D. 1998 . “Bayesian Statistics in Medicine: Where We are and Where We Should be Going” . Sankhya , 60 : 176 – 195 . Ser. B
   Google Scholar
• Tanner , M. A. 1993 . Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, , 2nd ed. , New York : Springer Verlag .
   Google Scholar
• Thiesson , B. , Meek , C. , Chickering , D. M. and Heckerman , D. 1999 . “Computationally Efficient Methods for Selecting Among Mixtures of Graphical Models,” . In Bayesian Statistics 6 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 631 – 656 . London : Oxford University Press .
   Google Scholar
• Tierney , L. 1991 . Lisp-Stat, An Object-Oriented Environment for Statistical Computing and Dynamic Graphics , New York : Wiley .
   Google Scholar
• Walley , P. 1991 . Statistical Reasoning With Imprecise Probabilities , London : Chapman and Hall .
   Google Scholar
• West , M. and Harrison , J. 1997 . Bayesian Forecasting and Dynamic Models, , 2nd ed. , New York : Springer-Verlag .
   Google Scholar
• Winkler , R. L. 1972 . Introduction to Bayesian Inference and Decision , New York : Holt, Rinehart, and Winston .
   Google Scholar
• Wolpert , R. L. and Ickstadt , K. 1998 . “Poisson/Gamma Random Field Models for Spatial Statistics” . Biometrika , 82 : 251 – 267 .
   Web of Science ®Google Scholar
• Yang , R. and Berger , J. 1997 . “A Catalogue of Noninformative Priors,” , Duke University . ISDS Discussion Paper 97–42
   Google Scholar
• Zellner , A. 1971 . An Introduction to Bayesian Inference in Econometrics , New York : Wiley .
   Google Scholar