Approximate Bayes Factors When a Mode Occurs on the Boundary

Journal of the American Statistical Association

Volumn 92, Issue 438, 1997, Pages 656-663

  Hsiao, Chuhsing Kate ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

Extrabinomial variation; Laplace's method; Schwarz criterion

Indexed keywords

EID: 0031536512     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1997.10474017     Document Type: Article

References (25)

1. Akaike, H. (1974), "A New Look at the Statistical Identification Model," IEEE Transactions on Automatic Control, 19,716-723.
2. Berger, J. O., and Delampady, M. (1987), "Testing Precise Hypotheses," Statistical Science, 2, 317-352.
3. Bleistein, N., and Handelsman, R. A. (1975), Asymptotic Expansions of Integrals, New York: Dover.
4. Box, G. E., and Tiao, G. C. (1972), Bayesian Inference in Statistical Analysis, Reading, MA: Addison-Wesley.
5. Erkanli, A. (1994), "Laplace Approximations for Posterior Expectations When the Mode Occurs at the Boundary of the Parameter Space;' Journal of the American Statistical Association, 89, 250-258.
6. Haughton, D. M. A. (1988), "On the Choice of a Model to Fit Data From an Exponential Family," Annals of Statistics, 16, 342-355.
7. Hsiao, C. K. (1994), "Bayesian Tests of Extra-Binomial Variability With Emphasis on the Boundary Case," unpublished Ph.D. dissertation, Carnegie Mellon University, Dept. of Statistics.
8. International Mathematical and Statistical Libraries, Inc. (1989), IMSL Library, Houston: Author.
9. Jeffreys, H. (1961), Theory of Probability (3rd ed.), London: Oxford University Press.
10. Kass, R. E., and Raftery, A. E. (1995), "Bayes Factors," Journal of the' American Statistical Association, 90, 773-795.
11. Kass, R. E., Tierney, L., and Kadane, J. B. (1990), ''The Validity of Posterior Asymptotic Expansions Based on Laplace's Method," in Bayesian and Likelihood Methods in Statistics and Econometrics, eds. S. Geisser, J. S. Hodges, S. J. Press, and A. Zellner. New York: North-Holland.
12. Kass, R. E., and Vaidyanathan, S. K. (1992), "Approximate Bayes Factors and Orthogonal Parameters, With Application to Testing Equality of Two Binomial Proportions," Journal of the Royal Statistical Society, Ser. B, 54, 129-144.
13. Kass, R. E., and Wasserman, L. (1995), "A Reference Bayesian Test for Nested Hypotheses and Its Relationship to the Schwarz Criterion," Journal of the American Statistical Association, 90, 928-934.
14. Lindley, D. V. (1957), "A Statistical Paradox," Biometrika, 44, 187-192.
15. Lindley, D. V (1980), "Approximate Bayesian Methods," in Bayesian Statistics, eds. J. M. Bernardo, M. H. DeGroot, D. V. Lindley, and A. M. E Smith, Valencia, Spain: University Press.
16. Mosteller, E, and Wallace, D. L. (1984), Applied Bayesian and Classical Inference (2nd ed.), New York: Springer-Verlag.
17. Olver, E (1974), Asymptotics and Special Functions, New York: Academic Press.
18. Prentice, R. L. (1986), "Binary Regression Using an Extended BetaBinomial Distribution, With Discussion of Correlation Induced by Covariate Measurement Errors," Journal of the American Statistical Association, 81, 321-327.
19. Raftery, A. E. (1986), "Choosing Models for Cross-Classifications," American Sociological Review, 51, 145-146.
20. Raftery, A. E (1988), "Approximate Bayes Factors for Generalized Linear Models," Technical Report 121, University of Washington, Dept. of Statistics.
21. Schwarz, G. (1978), "Estimating the Dimension of a Model," The Annals of Statistics, 6, 461-464.
22. Smith, A. M. E, and Spiegelhalter, D. J. (1980), "Bayes Factors and Choice Criteria for Linear Models," Journal ofthe Royal Statistical Society, Ser. B, 42, 213-220.
23. Tarone, R. E. (1979), ''Testing the Goodness-of-Fit of the Binomial Distribution," Biometrika, 66, 585-590.
24. Tierney, L., and Kadane, J. B. (1986), "Accurate Approximations for Posterior Moments and Marginal Densities," Journal of the American Statistical Association, 81, 82-86.
25. Williams, D. A. (1982), "Extra-Binomial Variation in Logistic Linear Models," Applied Statistics, 31,144-148.