Penalized loss functions for Bayesian model comparison

Biostatistics

Volumn 9, Issue 3, 2008, Pages 523-539

  Plummer, Martyn ^a  

^a INTERNATIONAL AGENCY FOR RESEARCH ON CANCER   (France)

Author keywords

Bayesian model comparison; Deviance information criterion; Disease mapping; Markov chain Monte Carlo methods; Mixture models

Indexed keywords

ARYLAMINE ACETYLTRANSFERASE; NAT2 PROTEIN, HUMAN;

ACETYLATION; ARTICLE; BAYES THEOREM; BIOLOGICAL MODEL; BIOMETRY; COHORT ANALYSIS; CONFIDENCE INTERVAL; DECISION THEORY; EPIDEMIOLOGY; FACTORIAL ANALYSIS; FORECASTING; GENETICS; HUMAN; LIP TUMOR; MALE; METABOLISM; METHODOLOGY; MONTE CARLO METHOD; PROBABILITY; RARE DISEASE; REFERENCE VALUE; REGRESSION ANALYSIS; STATISTICAL MODEL; STATISTICS; UNITED KINGDOM;

ACETYLATION; ARYLAMINE N-ACETYLTRANSFERASE; BAYES THEOREM; BIAS (EPIDEMIOLOGY); BIOMETRY; COHORT STUDIES; CONFIDENCE INTERVALS; DECISION THEORY; FACTOR ANALYSIS, STATISTICAL; FORECASTING; HUMANS; LIP NEOPLASMS; MALE; MARKOV CHAINS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MONTE CARLO METHOD; RARE DISEASES; REFERENCE VALUES; REGRESSION ANALYSIS; RESEARCH DESIGN; SCOTLAND;

EID: 45849088346     PISSN: 14654644     EISSN: 14684357     Source Type: Journal    
DOI: 10.1093/biostatistics/kxm049     Document Type: Article

References (48)

1. AITKIN, M. (1991). Posterior Bayes factors (with discussion). Journal of the Royal Statistical Society, Series B 53, 111-142.
2. BANERJEE, S., CARLIN, B. AND GELFAND, A. (2004). Hierarchical Modeling and Analysis for Spatial Data. Boca Raton, FL: Chapman & Hall/CRC.
3. BECHTEL, Y., BONAITI-PELLIE, C., POISSON, N., MAGNETTE, J. AND BECHTEL, P. (1993). A population and family study of n-acetyltransferase using caffeine urinary metabolites. Clinical Pharmacology and Therapeutics 54, 134-141.
4. BERGER, J. AND PERICCHI, L. (1996). The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 91, 109-122.
5. BERNARDO, J. (1979). Expected information as expected utility. The Annals of Statistics 7, 686-690.
6. BERNARDO, J. AND SMITH, A. (2000). Bayesian Theory. Chichister, UK: Wiley.
7. BESAG, J., YORK, J. AND MOLLIÉ , A. (1991). Bayesian image restoration with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics 43, 1-59.
8. BRESLOW, N. AND CLAYTON, D. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9-24.
9. BURNHAM, K. AND ANDERSON, D. (2000). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd edition. New York: Springer.
10. CELEUX, G., FORBES, F., ROBERT, C. AND TITTERINGTON, D. (2006a). Deviance information criteria for missing data models. Bayesian Analysis 1, 651-706.
11. CELEUX, G., FORBES, F., ROBERT, C. AND TITTERINGTON, D. (2006b). Rejoinder to discussion of deviance information criteria for missing data models. Bayesian Analysis 1, 701-706.
12. CELEUX, G., HURN, M. AND ROBERT, C. (2000). Computational and inferential difficulties with mixture posterior distributions. Journal of the American Statistical Association 95, 957-970.
13. CLAYTON, D. AND KALDOR, J. (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43, 671-681.
14. CLEMENTS, M., ARMSTRONG, B. AND MOOLGAVKAR, S. (2005). Lung cancer rate predictions using generalized additive models. Biostatistics 6, 576-589.
15. DANIELS, M. AND NORMAND, S. (2006). Longitudinal profiling of health care units based on continuous and discrete patient outcomes. Biostatistics 7, 1-15.
16. EFRON, B. (1983). Estimating the error rate of a prediction rule: improvements on cross-validation. Journal of the American Statistical Association 78, 316-331.
17. EFRON, B. (1986). How biased is the apparent error rate of a prediction rule? Journal of the American Statistical Association 81, 461-470.
18. ELLIOTT, M., GALLO, J., HAVE, T. T., BOGNER, H. AND KATZ, I. (2005). Using a Bayesian latent growth curve model to identify trajectories of positive affect and negative events following myocardial infarction. Biostatistics 6, 119-143.
19. GEISSER, S. AND EDDY, W. (1979). A predictive approach to model selection. Journal of the American Statistical Association 74, 153-160.
20. GELFAND, A. AND DEY, D. (1994). Bayesian model choice: asymptotics and exact calculations. Journal of the Royal Statistical Society, Series B 56, 501-514.
21. GELFAND, A. AND GHOSH, S. (1998). Model choice: a minimum posterior predictive loss approach. Biometrika 85, 1-11.
22. GELMAN, A., CARLIN, J., STERN, H. AND RUBIN, D. (2002). Bayesian Data Analysis, 2nd edition. Boca Raton, FL: Chapman & Hall/CRC.
23. GNEITING, T. AND RAFTERY, A. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association 102, 359-378.
24. HEIN, D., DOLL, M., FRETLAND, A., LEFF, M., WEBB, S., XIAO, G., DEVANABOYINA, U., NANGJU, N. AND FENG, Y. (2000). Molecular genetics and epidemiology of the NAT1 and NAT2 acetylation polymorphisms. Cancer Epidemiology, Biomarkers and Prevention 9, 29-42.
25. HURVICH, C. AND TSAI, C.-L. (1989). Regression and time series model selection in small samples. Biometrika 76, 297-307.
26. KASS, R. E. AND RAFTERY, A. E. (1995). Bayes factors. Journal of the American Statistical Association 90, 773-795.
27. KEMP, I., BOYLE, P., SMANS, M. AND MUIR, C. (1985). Atlas of Cancer Incidence in Scotland, 1975-80. Incidence and Epidemiological Perspective. IARC Scientific Publications, Number 72. Lyon, France: International Agency for Research on Cancer.
28. LAUD, P. AND IBRAHIM, J. (1995). Predictive model selection. Journal of the Royal Statistical Society, Series B 57, 247-262.
29. LINDLEY, D. (1991). Discussion of the paper by Aitkin. Journal of the Royal Statistical Society, Series B 53, 130-131.
30. LINDLEY, D. AND SMITH, A. (1972). Bayes estimates for the linear model (with discussion). Journal of the Royal Statistical Society, Series B 34, 1-44.
31. LIU, X., WALL, M. AND HODGES, J. (2005). Generalized spatial structural equation models. Biostatistics 6, 539-557.
32. MARSHALL, E. AND SPIEGELHALTER, D. (2003). Approximate cross-validatory predictive checks in disease mapping models. Statistics in Medicine 22, 1649-1660.
33. NEAL, R. (1996). Sampling from multimodal distributions using tempered transitions. Statistics and Computing 4, 353-366.
34. O'HAGAN, A. (1995). Fractional Bayes factors for model comparison (with discussion). Journal of the Royal Statistical Society, Series B 57, 99-138.
35. PERUGGIA, M. (1997). On the variability of case-deletion importance sampling weights in the Bayesian linear model. Journal of the American Statistical Association 92, 199-207.
36. PLUMMER, M. (2002). Discussion of the paper by Spiegelhalter et al. Journal of the Royal Statistical Society, Series B 64, 620.
37. PLUMMER, M. (2006). Comment on article by Celeux et al. Bayesian Analysis 1, 681-686.
38. RICHARDSON, S. AND GREEN, P. (1997). On Bayesian analysis of mixtures with an unknown number of components (with discussion). Journal of the Royal Statistical Society, Series B 59, 731-758.
39. RIPLEY, B. (1996). Statistical Pattern Recognition and Neural Networks. Cambridge, UK: Cambridge University Press.
40. SPIEGELHALTER, D., BEST, N. AND CARLIN, B. (1998). Bayesian deviance, the effective number of parameters, and the comparison of arbitrarily complex models. Technical Report 98-009. Division of Biostatistics, University of Minnesota. Cambridge, UK: Medical Research Council Biostatistics Unit.
41. SPIEGELHALTER, D., BEST, N., CARLIN, B. AND VAN DER LINDE, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society, Series B 64, 583-639.
42. SPIEGELHALTER, D. J., THOMAS, A., BEST, N. AND LUNN, D. (2004). WinBUGS User Manual, Version 2.0.
43. STONE, M. (1977). An asymptotic equivalence of choice of model cross-validation and Akaike's criterion. Journal of the Royal Statistical Society, Series B 36, 44-47.
44. STONE, M. (2002). Discussion of the paper by Spiegelhalter et al. Journal of the Royal Statistical Society, Series B 64, 621.
45. VAN DER LINDE, A. (2004). On the association between a random parameter and an observation. Test 13, 85-111.
46. VAN DER LINDE, A. (2005). DIC in variable selection. Statistica Neerlandica 59, 45-56.
47. VEHTARI, A. (2001). Bayesian model assessment and selection using expected utilities, [PhD. Thesis]. Helsinki, Finland: Helsinki University of Technology.
48. VEHTARI, A. AND LAMPINEN, J. (2002). Bayesian model assessment and comparison using cross-validation predictive densities. Neural Computation 14, 2439-2468.