Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives

Journal of the American Statistical Association

Volumn 96, Issue 453, 2001, Pages 174-184

  Berger, James O ^a   Guglielmi, Alessandra ^b  

^a DUKE UNIVERSITY   (United States)

^b CNR   (Italy)

Author keywords

Bayes factor; Bayesian robustness; Conditional frequentist type I and type II error probabilities; Noninformative priors; Nonparametric bayes; Polya tree process; Testing fit

Indexed keywords

EID: 1842715165     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1198/016214501750333045     Document Type: Article

References (24)

1. Andrews, D. F., and Herzberg, A. M. (1985), Data, New York: Springer-Verlag.
2. Barron, A., Schervish, M. J., and Wasserman, L. (1999), “The Consistency of Posterior Distributions in Nonparametric Problems,” The Annals of Statistics, 27, 536–561.
3. Bayarri, M. J., and Berger, J. O. (1999), “Quantifying Surprise in the Data and Model Verification,” in Bayesian Statistics (Vol. 6), eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, London: Oxford University Press, pp. 53–82.
4. Berger, J. O., Boukai, B., and Wang, W. (1997), “Unified Frequentist and Bayesian Testing of Precise Hypotheses,” Statistical Science, 12, 133–160.
5. Berger, J. O., Brown, L. D., and Wolpert, R. L. (1994), “A Unified Conditional Frequentist and Bayesian Test for Fixed and Sequential Simple Hypothesis Testing,” The Annals of Statistics, 22, 1787–1807.
6. Berger, J. O., and Pericchi, L. R. (1996), “On the Justification of Default and Intrinsic Bayes Factors,” in Modelling and Prediction, eds. J. C. Lee, W. Johnson, and A. Zellner, New York: Springer-Verlag, pp. 276–293.
7. Berger, J. O., and Pericchi, L. R. (1998), “Accurate and Stable Bayesian Model Selection: The Median Intrinsic Bayes Factor,” Sankhyā Ser. B, 60, 1–16.
8. Berger, J. O., Pericchi, L. R., and Varshavsky, J. A. (1998), “Bayes Factors and Marginal Distributions in Invariant Situations,” Sankhyā Ser. A, 60, 307–321.
9. Carota, C., and Parmigiani, G. (1996), “On Bayes Factors for Nonparametric Alternatives,” in Bayesian Statistics (Vol. 5), eds. J. M. Bernardo J. O. Berger, A. P. Dawid, and A. F. M. Smith, London: Oxford University Press, pp. 507–511.
10. Dass, S., and Berger, J. (1998), “Unified Bayesian and Conditional Frequentist Testing of Composite Hypotheses,” Discussion Paper 98-43, Duke University, Institute of Statistics and Decision Sciences.
11. Delampady, M., and Berger, J. O. (1990), “Lower Bounds on Bayes Factors for Multinomial Distributions, with Application to Chi-Squared Tests of Fit,” The Annals of Statistics, 18, 1295–1316.
12. Draghici, L., and Ramamoorthi, R. V. (in press), “A Note on the Absolute Continuity and Singularity of Polya Tree Priors and Posteriors,” in The Scandanavian Journal of Statistics.
13. Fabius, J. (1964), “Asymptotic Behaviour of Bayes’ Estimate,” Annals of Mathematical Statistics, 35, 846–856.
14. Ferguson, T. S. (1974), “Prior Distributions on Spaces of Probability Measures,” The Annals of Statistics, 2, 615–629.
15. Florens, J. P., Richard, J. F., and Rolin, J. M. (1996), “Bayesian Encompassing Specification Tests of a Parametric Model Against a Nonparametric Alternative,” Technical Report 96.08, Université Catholique de Louvain, Institut de Statistique.
16. Freedman, D. (1963), “On the Asymptotic Behaviour of Bayes’ Estimate in the Discrete Case,” Annals of Mathematical Statistics, 34, 1194–1216.
17. Geweke, J. (1989), “Bayesian Inference in Econometric Models Using Monte Carlo Integration,” Econometrica, 57, 1317–1339.
18. Lavine, M. (1992), “Some Aspects of Polya Tree Distributions for Statistical Modelling,” The Annals of Statistics, 20, 1222–1235.
19. Lavine, M. (1994), “More Aspects of Polya Tree Distributions for Statistical Modelling,” The Annals of Statistics, 22, 1161–1176.
20. MacEachern, S. N. (1998), “Estimation of Bayes Factors in Mixture of Dirichlet Process Models,” Technical Report, Ohio State University.
21. Mauldin, R. D., Sudderth, W. D., and Williams, S. C. (1992), “Polya Trees and Random Distributions,” The Annals of Statistics, 20, 1203–1221.
22. Sellke, T., Bayarri, M. J., and Berger, J. O. (in press), “Calibration of PValues for Precise Null Hypotheses,” The American Statistician.
23. Verdinelli, I., and Wasserman, L. (1998), “Bayesian Goodness of Fit Testing Using Infinite Dimensional Exponential Families,” The Annals of Statistics, 20, 1203–1221.
24. Viele, K. (1996), “A Nonparametric Bayesian Method for Evaluating Fit in Hierarchical Curve Models,” Technical Report 96.358, University of Kentucky, Dept. of Statistics.