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Model uncertainty. (English) Zbl 1062.62044
Summary: The evolution of Bayesian approaches for model uncertainty over the past decade has been remarkable. Catalyzed by advances in methods and technology for posterior computation, the scope of these methods has widened substantially. Major thrusts of these developments have included new methods for semiautomatic prior specification and posterior exploration. To illustrate key aspects of this evolution, the highlights of some of these developments are described.

MSC:
62F15 Bayesian inference
65C40 Numerical analysis or methods applied to Markov chains
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[1] Abramovich, F., Sapatinas, T. and Silverman, B. W. (1998). Wavelet thresholding via a Bayesian approach. J. R. Stat. Soc. Ser. B Stat. Methodol. 60 725–749. JSTOR: · Zbl 0910.62031
[2] Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory (B. Petrov and F. Csáki, eds.) 267–281. Akadémiai Kiadó, Budapest. · Zbl 0283.62006
[3] Andrieu, C., Doucet, A. and Robert, C. (2004). Computational advances for and from Bayesian analysis. Statist. Sci. 19 118–127. · Zbl 1062.62043
[4] Atay-Kayis, A. and Massam, H. (2002). The marginal likelihood for decomposable and nondecomposable graphical Gaussian models. Technical report, Dept. Mathematics, York Univ. · Zbl 1094.62028
[5] Barbieri, M. M. and Berger, J. (2004). Optimal predictive model selection. Ann. Statist. 32 870–897. · Zbl 1092.62033
[6] Bartlett, M. (1957). A comment on D. V. Lindley’s statistical paradox. Biometrika 44 533–534. · Zbl 0073.35702
[7] Berger, J. O., Ghosh, J. K. and Mukhopadhyay, N. (2003). Approximations and consistency of Bayes factors as model dimension grows. J. Statist. Plann. Inference 112 241–258. · Zbl 1026.62018
[8] Berger, J. O. and Pericchi, L. R. (1996a). The intrinsic Bayes factor for linear models. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 25–44. Oxford Univ. Press. · Zbl 0870.62021
[9] Berger, J. O. and Pericchi, L. R. (1996b). The intrinsic Bayes factor for model selection and prediction. J. Amer. Statist. Assoc. 91 109–122. JSTOR: · Zbl 0870.62021
[10] Berger, J. O. and Pericchi, L. R. (1998). Accurate and stable Bayesian model selection: The median intrinsic Bayes factor. Sankhyā Ser. B 60 1–18. · Zbl 1081.62517
[11] Berger, J. O. and Pericchi, L. (2001). Objective Bayesian methods for model selection: Introduction and comparison (with discussion). In Model Selection (P. Lahiri, ed.) 135–207. IMS, Beachwood, OH.
[12] Bernardo, J. M. and Smith, A. F. M. (1994). Bayesian Theory . Wiley, New York. · Zbl 0796.62002
[13] Besag, J. and Green, P. J. (1993). Spatial statistics and Bayesian computation (with discussion). J. Roy. Statist. Soc. Ser. B 55 25–37. JSTOR: · Zbl 0800.62572
[14] Breiman, L., Friedman, J. H., Olshen, R. A. and Stone, C. J. (1984). Classification and Regression Trees . Wadsworth, Belmont, CA. · Zbl 0541.62042
[15] Brooks, S. P., Giudici, P. and Roberts, G. O. (2003). Efficient construction of reversible jump Markov chain Monte Carlo proposal distributions (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 65 3–55. JSTOR: · Zbl 1063.62120
[16] Brown, P. J., Fearn, T. and Vannucci, M. (1999). The choice of variables in multivariate regression: A non-conjugate Bayesian decision theory approach. Biometrika 86 635–648. JSTOR: · Zbl 1072.62510
[17] Brown, P. J., Vannucci, M. and Fearn, T. (1998). Multivariate Bayesian variable selection and prediction. J. R. Stat. Soc. Ser. B Stat. Methodol. 60 627–641. JSTOR: · Zbl 0909.62022
[18] Brown, P. J., Vannucci, M. and Fearn, T. (2002). Bayes model averaging with selection of regressors. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 519–536. JSTOR: · Zbl 1073.62004
[19] Buntine, W. (1992). Learning classification trees. Statist. Comput. 2 63–73.
[20] Carlin, B. P. and Chib, S. (1995). Bayesian model choice via Markov chain Monte Carlo methods. J. Roy. Statist. Soc. Ser. B 57 473–484. · Zbl 0827.62027
[21] Casella, G. and Moreno, E. (2002). Objective Bayes variable selection. Technical Report 2002-023, Dept. Statistics, Univ. Florida.
[22] Chen, M.-H. (1994). Importance-weighted marginal Bayesian posterior density estimation. J. Amer. Statist. Assoc. 89 818–824. JSTOR: · Zbl 0804.62040
[23] Chen, M.-H., Ibrahim, J. G., Shao, Q.-M. and Weiss, R. E. (2003). Prior elicitation for model selection and estimation in generalized linear mixed models. J. Statist. Plann. Inference 111 57–76. · Zbl 1027.62056
[24] Chen, M.-H., Ibrahim, J. G. and Yiannoutsos, C. (1999). Prior elicitation, variable selection and Bayesian computation for logistic regression models. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 223–242. JSTOR: · Zbl 0913.62026
[25] Chen, M.-H. and Shao, Q.-M. (1997). On Monte Carlo methods for estimating ratios of normalizing constants. Ann. Statist. 25 1563–1594. · Zbl 0936.62028
[26] Chen, M.-H., Shao, Q.-M. and Ibrahim, J. G. (2000). Monte Carlo Methods in Bayesian Computation . Springer, New York. · Zbl 0949.65005
[27] Chib, S. (1995). Marginal likelihood from the Gibbs output. J. Amer. Statist. Assoc. 90 1313–1321. JSTOR: · Zbl 0868.62027
[28] Chib, S. and Jeliazkov, I. (2001). Marginal likelihood from the Metropolis–Hastings output. J. Amer. Statist. Assoc. 96 270–281. JSTOR: · Zbl 1015.62020
[29] Chipman, H. A. (1996). Bayesian variable selection with related predictors. Canad. J. Statist. 24 17–36. JSTOR: · Zbl 0849.62032
[30] Chipman, H. A., George, E. I. and McCulloch, R. E. (1998). Bayesian CART model search (with discussion). J. Amer. Statist. Assoc. 93 935–960. JSTOR: · Zbl 1072.62650
[31] Chipman, H. A., George, E. I. and McCulloch, R. E. (2001). The practical implementation of Bayesian model selection (with discussion). In Model Selection (P. Lahiri, ed.) 65–134. IMS, Beachwood, OH.
[32] Chipman, H. A., George, E. I. and McCulloch, R. E. (2003). Bayesian treed generalized linear models (with discussion). In Bayesian Statistics 7 (J. M. Bernardo, M. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.) 85–103. Oxford Univ. Press.
[33] Chipman, H. A., Kolaczyk, E. D. and McCulloch, R. E. (1997). Adaptive Bayesian wavelet shrinkage. J. Amer. Statist. Assoc. 92 1413–1421. · Zbl 0913.62027
[34] Clyde, M. (1999). Bayesian model averaging and model search strategies (with discussion). In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 157–185. Oxford Univ. Press. · Zbl 0973.62022
[35] Clyde, M. (2001). Discussion of “The practical implementation of Bayesian model selection,” by H. A. Chipman, E. I. George and R. E. McCulloch. In Model Selection (P. Lahiri, ed.) 117–124. IMS, Beachwood, OH.
[36] Clyde, M., DeSimone, H. and Parmigiani, G. (1996). Prediction via orthogonalized model mixing. J. Amer. Statist. Assoc. 91 1197–1208. · Zbl 0880.62026
[37] Clyde, M. and George, E. I. (2000). Flexible empirical Bayes estimation for wavelets. J. R. Stat. Soc. Ser. B Stat. Methodol. 62 681–698. JSTOR: · Zbl 0957.62006
[38] Clyde, M., Parmigiani, G. and Vidakovic, B. (1998). Multiple shrinkage and subset selection in wavelets. Biometrika 85 391–401. JSTOR: · Zbl 0938.62021
[39] Cui, W. (2002). Variable selection: Empirical Bayes vs. fully Bayes. Ph.D. dissertation, Dept. Management Science and Information Systems, Univ. Texas, Austin. · Zbl 1130.62007
[40] Dawid, A. and Lauritzen, S. (2001). Compatible prior distributions. In Bayesian Methods with Applications to Science, Policy , and Official Statistics, Selected Papers from ISBA 2000: The Sixth World Meeting of the International Society for Bayesian Analysis (E. I. George, ed.) 109–118. Eurostat, Luxembourg.
[41] Dellaportas, P. and Forster, J. J. (1999). Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models. Biometrika 86 615–633. JSTOR: · Zbl 0949.62050
[42] Dellaportas, P., Forster, J. J. and Ntzoufras, I. (2002). On Bayesian model and variable selection using MCMC. Statist. Comput. 12 27–36. · Zbl 1247.62086
[43] Dellaportas, P., Giudici, P. and Roberts, G. (2003). Bayesian inference for nondecomposable graphical Gaussian models. Sankhyā Ser. A . 65 43–55. · Zbl 1192.62090
[44] Dempster, A. M. (1972). Covariance selection. Biometrics 28 157–175.
[45] Denison, D. G. T., Holmes, C., Mallick, B. K. and Smith, A. F. M. (2002). Bayesian Methods for Nonlinear Classification and Regression . Wiley, New York. · Zbl 0994.62019
[46] Denison, D. G. T., Mallick, B. K. and Smith, A. F. M. (1998a). Automatic Bayesian curve fitting. J. R. Stat. Soc. Ser. B Stat. Methodol. 60 333–350. JSTOR: · Zbl 0907.62031
[47] Denison, D. G. T., Mallick, B. K. and Smith, A. F. M. (1998b). A Bayesian CART algorithm. Biometrika 85 363–377. JSTOR: · Zbl 1048.62502
[48] Denison, D. G. T., Mallick, B. K. and Smith, A. F. M. (1998c). Bayesian MARS. Statist. Comput. 8 337–346.
[49] DiCiccio, T. J., Kass, R. E., Raftery, A. and Wasserman, L. (1997). Computing Bayes factors by combining simulation and asymptotic approximations. J. Amer. Statist. Assoc. 92 903–915. JSTOR: · Zbl 1050.62520
[50] Draper, D. (1995). Assessment and propagation of model uncertainty (with discussion). J. Roy. Statist. Soc. Ser. B 57 45–97. JSTOR: · Zbl 0812.62001
[51] Draper, D. and Fouskakis, D. (2000). A case study of stochastic optimization in health policy: Problem formulation and preliminary results. J. Global Optimization 18 399–416. · Zbl 1179.90244
[52] Dupuis, J. A. and Robert, C. P. (2003). Variable selection in qualitative models via an entropic explanatory power. J. Statist. Plann. Inference 111 77–94. · Zbl 1033.62066
[53] Fernández, C., Ley, E. and Steel, M. F. (2001). Benchmark priors for Bayesian model averaging. J. Econometrics 100 381–427. · Zbl 1091.62507
[54] Foster, D. P. and George, E. I. (1994). The risk inflation criterion for multiple regression. Ann. Statist. 22 1947–1975. JSTOR: · Zbl 0829.62066
[55] Furnival, G. M. and Wilson, R. W., Jr. (1974). Regression by leaps and bounds. Technometrics 16 499–511. · Zbl 0285.05110
[56] Geisser, S. (1993). Predictive Inference. An Introduction . Chapman and Hall, London. · Zbl 0824.62001
[57] Gelfand, A. E., Dey, D. K. and Chang, H. (1992). Model determination using predictive distributions, with implementation via sampling-based methods (with discussion). In Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 147–167. Oxford Univ. Press.
[58] Gelfand, A. E. and Ghosh, S. K. (1998). Model choice: A minimum posterior predictive loss approach. Biometrika 85 1–11. JSTOR: · Zbl 0904.62036
[59] Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398–409. JSTOR: · Zbl 0702.62020
[60] Gelman, A. and Meng, X.-L. (1998). Simulating normalizing constants: From importance sampling to bridge sampling to path sampling. Statist. Sci. 13 163–185. · Zbl 0966.65004
[61] George, E. I. (1999). Discussion of “Bayesian model averaging and model search strategies,” by M. Clyde. In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 175–177. Oxford Univ. Press. · Zbl 0973.62022
[62] George, E. I. (2000). The variable selection problem. J. Amer. Statist. Assoc. 95 1304–1308. JSTOR: · Zbl 1018.62050
[63] George, E. I. and Foster, D. P. (2000). Calibration and empirical Bayes variable selection. Biometrika 87 731–747. JSTOR: · Zbl 1029.62008
[64] George, E. I. and McCulloch, R. E. (1993). Variable selection via Gibbs sampling. J. Amer. Statist. Assoc. 88 881–889.
[65] George, E. I. and McCulloch, R. E. (1997). Approaches for Bayesian variable selection. Statist. Sinica 7 339–374. · Zbl 0884.62031
[66] George, E. I., McCulloch, R. and Tsay, R. (1996). Two approaches to Bayesian model selection with applications. In Bayesian Analysis in Statistics and Econometrics: Essays in Honor of Arnold Zellner (D. Berry, K. Chaloner and J. Geweke, eds.) 339–348. Wiley, New York.
[67] Geweke, J. (1996). Variable selection and model comparison in regression. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 609–620. Oxford Univ. Press.
[68] Giudici, P. and Green, P. J. (1999). Decomposable graphical Gaussian model determination. Biometrika 86 785–801. JSTOR: · Zbl 0940.62019
[69] Godsill, S. J. (2001). On the relationship between Markov chain Monte Carlo methods for model uncertainty. J. Comput. Graph. Statist. 10 230–248. JSTOR: · Zbl 04567021
[70] Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711–732. JSTOR: · Zbl 0861.62023
[71] Green, P. J. (2003). Trans-dimensional Markov chain Monte Carlo. In Highly Structured Stochastic Systems (P. J. Green, N. L. Hjort and S. Richardson, eds.) 179–206. Oxford Univ. Press.
[72] Han, C. and Carlin, B. P. (2001). Markov chain Monte Carlo methods for computing Bayes factors: A comparative review. J. Amer. Statist. Assoc. 96 1122–1132.
[73] Hansen, M. H. and Kooperberg, C. (2002). Spline adaptation in extended linear models (with discussion). Statist. Sci. 17 2–51. · Zbl 1013.62044
[74] Hansen, M. H. and Yu, B. (2001). Model selection and the principle of minimum description length. J. Amer. Statist. Assoc. 96 746–774. JSTOR: · Zbl 1017.62004
[75] Hodges, J. S. (1987). Uncertainty, policy analysis and statistics (with discussion). Statist. Sci. 2 259–275.
[76] Hoeting, J. A., Madigan, D., Raftery, A. E. and Volinsky, C. T. (1999). Bayesian model averaging: A tutorial (with discussion). Statist. Sci. 14 382–417. (Corrected version available at http://www.stat.washington. edu/www/research/online/hoeting1999.pdf.) · Zbl 1059.62525
[77] Hoeting, J. A., Raftery, A. E. and Madigan, D. (2002). Bayesian variable and transformation selection in linear regression. J. Comput. Graph. Statist. 11 485–507. JSTOR:
[78] Ibrahim, J. G., Chen, M.-H. and MacEachern, S. N. (1999). Bayesian variable selection for proportional hazards models. Canad. J. Statist. 27 701–717. JSTOR: · Zbl 0957.62018
[79] Ibrahim, J. G., Chen, M.-H. and Ryan, L. M. (2000). Bayesian variable selection for time series count data. Statist. Sinica 10 971–987. · Zbl 0952.62081
[80] Johnstone, I. and Silverman, B. (2004). Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences. Ann. Statist. 32 1594–1649. · Zbl 1047.62008
[81] Jordan, M. I. (2004). Graphical models. Statist. Sci. 19 140–155. · Zbl 1057.62001
[82] Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90 773–795. · Zbl 0846.62028
[83] Key, J. T., Pericchi, L. R. and Smith, A. F. M. (1999). Bayesian model choice: What and why? In Bayesian Statistics 6 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 343–370. Oxford Univ. Press. · Zbl 0956.62007
[84] Kohn, R., Marron, J. S. and Yau, P. (2000). Wavelet estimation using Bayesian basis selection and basis averaging. Statist. Sinica 10 109–128. · Zbl 0970.62020
[85] Leamer, E. E. (1978a). Regression selection strategies and revealed priors. J. Amer. Statist. Assoc. 73 580–587. · Zbl 0391.62045
[86] Leamer, E. E. (1978b). Specification Searches: Ad Hoc Inference with Nonexperimental Data . Wiley, New York. · Zbl 0384.62089
[87] Lewis, S. M. and Raftery, A. E. (1997). Estimating Bayes factors via posterior simulation with the Laplace–Metropolis estimator. J. Amer. Statist. Assoc. 92 648–655. JSTOR: · Zbl 0889.62018
[88] Liang, F., Paulo, R., Molina, G., Clyde, M. and Berger, J. (2003). Gaussian hyper-geometric and other mixtures of \(g\)-priors for Bayesian variable selection. Technical report, Statistical and Applied Mathematical Sciences Inst., Research Triangle Park, NC.
[89] Liang, F., Truong, Y. and Wong, W. H. (2001). Automatic Bayesian model averaging for linear regression and applications in Bayesian curve fitting. Statist. Sinica 11 1005–1029. · Zbl 0984.62018
[90] Lindley, D. V. (1968). The choice of variables in multiple regression (with discussion). J. Roy. Statist. Soc. Ser. B 30 31–66. JSTOR: · Zbl 0155.26702
[91] Madigan, D. and Raftery, A. E. (1994). Model selection and accounting for model uncertainty in graphical models using Occam’s window. J. Amer. Statist. Assoc. 89 1535–1546. · Zbl 0814.62030
[92] Madigan, D. and York, J. (1995). Bayesian graphical models for discrete data. Internat. Statist. Rev. 63 215–232. · Zbl 0834.62003
[93] Marriott, J. M., Spencer, N. M. and Pettitt, A. N. (2001). A Bayesian approach to selecting covariates for prediction. Scand. J. Statist. 28 87–97. · Zbl 0965.62024
[94] McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models , 2nd ed. Chapman and Hall, London. · Zbl 0588.62104
[95] Meng, X.-L. and Wong, W. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statist. Sinica 6 831–860. · Zbl 0857.62017
[96] Miller, A. J. (2002). Subset Selection in Regression , 2nd ed. Chapman and Hall, London. · Zbl 1051.62060
[97] Mitchell, T. J. and Beauchamp, J. J. (1988). Bayesian variable selection in linear regression (with discussion). J. Amer. Statist. Assoc. 83 1023–1032. JSTOR: · Zbl 0673.62051
[98] Müller, P. and Quintana, F. A. (2004). Nonparametric Bayesian data analysis. Statist. Sci. 19 95–110. · Zbl 1057.62032
[99] Ntzoufras, I., Dellaportas, P. and Forster, J. J. (2003). Bayesian variable and link determination for generalised linear models. J. Statist. Plann. Inference 111 165–180. · Zbl 1033.62026
[100] Ntzoufras, I., Forster, J. J. and Dellaportas, P. (2000). Stochastic search variable selection for log-linear models. J. Statist. Comput. Simulation 68 23–37. · Zbl 0968.62051
[101] O’Hagan, A. (1995). Fractional Bayes factors for model comparison (with discussion). J. Roy. Statist. Soc. Ser. B 57 99–138. JSTOR: · Zbl 0813.62026
[102] Pauler, D. K. (1998). The Schwarz criterion and related methods for normal linear models. Biometrika 85 13–27. JSTOR: · Zbl 1067.62550
[103] Pauler, D. K., Wakefield, J. C. and Kass, R. E. (1999). Bayes factors and approximations for variance component models. J. Amer. Statist. Assoc. 94 1242–1253. JSTOR: · Zbl 0998.62017
[104] Pérez, J. and Berger, J. O. (2000). Expected posterior prior distributions for model selection. Technical Report 00-08, Institute of Statistics and Decision Sciences, Duke Univ. · Zbl 1036.62026
[105] Raftery, A. E. (1996). Approximate Bayes factors and accounting for model uncertainty in generalised linear models. Biometrika 83 251–266. JSTOR: · Zbl 0864.62049
[106] Raftery, A. E., Madigan, D. and Hoeting, J. A. (1997). Bayesian model averaging for linear regression models. J. Amer. Statist. Assoc. 92 179–191. JSTOR: · Zbl 0888.62026
[107] Raftery, A. E., Madigan, D. and Volinsky, C. T. (1996). Accounting for model uncertainty in survival analysis improves predictive performance. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 323–349. Oxford Univ. Press.
[108] Roverato, A. (2002). Hyper inverse Wishart distribution for non-decomposable graphs and its application to Bayesian inference for Gaussian graphical models. Scand. J. Statist. 29 391–411. · Zbl 1036.62027
[109] San Martini, A. and Spezzaferri, F. (1984). A predictive model selection criterion. J. Roy. Statist. Soc. Ser. B 46 296–303. JSTOR: · Zbl 0566.62004
[110] Schwarz, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461–464. JSTOR: · Zbl 0379.62005
[111] Shively, T. S., Kohn, R. and Wood, S. (1999). Variable selection and function estimation in additive nonparametric regression using a data-based prior (with discussion). J. Amer. Statist. Assoc. 94 777–806. JSTOR: · Zbl 0994.62033
[112] Smith, A. F. M. and Roberts, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). J. Roy. Statist. Soc. Ser. B 55 3–23. JSTOR: · Zbl 0779.62030
[113] Smith, M. and Kohn, R. (1996). Nonparametric regression using Bayesian variable selection. J. Econometrics 75 317–343. · Zbl 0864.62025
[114] Smith, M. and Kohn, R. (1997). A Bayesian approach to nonparametric bivariate regression. J. Amer. Statist. Assoc. 92 1522–1535. JSTOR: · Zbl 0912.62052
[115] Smith, M. and Kohn, R. (2002). Parsimonious covariance matrix estimation for longitudinal data. J. Amer. Statist. Assoc. 97 1141–1153. JSTOR: · Zbl 1041.62044
[116] Stewart, L. and Davis, W. W. (1986). Bayesian posterior distributions over sets of possible models with inferences computed by Monte Carlo integration. The Statistician 35 175–182.
[117] Strawderman, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean. Ann. Math. Statist. 42 385–388. · Zbl 0222.62006
[118] Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). Ann. Statist. 22 1701–1728. JSTOR: · Zbl 0829.62080
[119] Tierney, L. and Kadane, J. (1986). Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81 82–86. JSTOR: · Zbl 0587.62067
[120] Verdinelli, I. and Wasserman, L. (1995). Computing Bayes factors using a generalization of the Savage–Dickey density ratio. J. Amer. Statist. Assoc. 90 614–618. JSTOR: · Zbl 0826.62022
[121] Volinsky, C. T., Madigan, D., Raftery, A. E. and Kronmal, R. A. (1997). Bayesian model averaging in proportional hazard models: Assessing the risk of a stroke. Appl. Statist. 46 433–448. · Zbl 0903.62093
[122] Wakefield, J. and Bennett, J. (1996). The Bayesian modeling of covariates for population pharmacokinetic models. J. Amer. Statist. Assoc. 91 917–927. · Zbl 0882.62104
[123] Wang, X. (2002). Bayesian variable selection for generalized linear models. Ph.D. dissertation, Dept. Management Science and Information Systems, Univ. Texas, Austin.
[124] Wolfe, P. J., Godsill, S. J. and Ng, W.-J. (2004). Bayesian variable selection and regularisation for time–frequency surface estimation. J. R. Stat. Soc. Ser. B Stat. Methodol. · Zbl 1046.62028
[125] Wong, F., Carter, C. and Kohn, R. (2003). Efficient estimation of covariance selection models. Biometrika 90 809–830. · Zbl 1436.62346
[126] Wood, S. and Kohn, R. (1998). A Bayesian approach to robust binary nonparametric regression. J. Amer. Statist. Assoc. 93 203–213. · Zbl 0906.62037
[127] Wood, S., Kohn, R., Shively, T. and Jiang, W. (2002). Model selection in spline nonparametric regression. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 119–139. JSTOR: · Zbl 1015.62039
[128] Zellner, A. (1984). Posterior odds ratios for regression hypotheses: General considerations and some specific results. In Basic Issues in Econometrics (A. Zellner, ed.) 275–305. Univ. Chicago Press.
[129] Zellner, A. (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 (P. K. Goel and A. Zellner, eds.) 233–243. North-Holland, Amsterdam. · Zbl 0655.62071
[130] Zellner, A. and Siow, A. (1980). Posterior odds ratios for selected regression hypotheses. In Bayesian Statistics. Proceedings of the First Valencia International Meeting Held in Valencia (Spain) (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 585–603. Valencia Univ. Press. · Zbl 0435.00013
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