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Probability model choice in single samples from exponential families using Poisson log-linear modelling, and model comparison using Bayes and posterior Bayes factors

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Abstract

This paper describes a method due to Lindsey (1974a) for fitting different exponential family distributions for a single population to the same data, using Poisson log-linear modelling of the density or mass function. The method is extended to Efron's (1986) double exponential family, giving exact ML estimation of the two parameters not easily achievable directly. The problem of comparing the fit of the non-nested models is addressed by both Bayes and posterior Bayes factors (Aitkin, 1991). The latter allow direct comparisons of deviances from the fitted distributions.

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References

  • Aitkin, M. (1987) Modelling variance heterogeneity in normal regression using GLIM. Applied Statistics, 36, 332–339.

    Google Scholar 

  • Aitkin, M. (1991) Posterior Bayes factors (with discussion). Journal of the Royal Statistical Society, B, 53, 111–142.

    Google Scholar 

  • Aitkin, M. (1992a) Model choice in contingency table analysis using the posterior Bayes factor. Computational Statistics and Data Analysis, 13, 245–251.

    Google Scholar 

  • Aitkin, M. (1992b) Evidence and the posterior Bayes factor. Mathematical Scientist, 17, 15–25.

    Google Scholar 

  • Aitkin, M. (1993) Posterior Bayes factor analysis for an exponential regression model. Statistics and Computing, 3, 17–22.

    Google Scholar 

  • Aitkin, M. and Fuchs, C. (1993) An analysis of models for the dilution and adulteration of fruit juice. Statistics and Computing 3, 89–99.

    Google Scholar 

  • Berger, J. O. and Perrichi, L. R. (1993) The intrinsic Bayes factor for model selection and prediction. Technical report #93-43C, Department of Statistics, Purdue University.

  • Cox, D. R. (1961) Tests of separate families of hypotheses. In Proceedings of the 4th Berkeley Symposium on Mathematics, Probability and Statistics, Vol. 1, pp. 105–123. University of California Press, Berkeley.

    Google Scholar 

  • Cox, D. R. (1962) Further results on tests of separate families of hypotheses. Journal of the Royal Statistical Society, B24, 406–424.

    Google Scholar 

  • Dey, D. K. and Chang, H. (1993) Measuring the effect of observations using posterior Bayes factor with vague prior information. Submitted for publication.

  • Efron, B. (1986) Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association, 81, 709–721.

    Google Scholar 

  • Efron, B. (1993) Bayes and likelihood calculations from confidence intervals. Biometrika, 80, 3–26.

    Google Scholar 

  • Gelfand, A. E. and Dalal, S. R. (1990) A note on overdispersed exponential families. Biometrika, 77, 55–64.

    Google Scholar 

  • Greenwood, M. and Yule, G. U. (1920) An inquiry into the nature of frequency-distributions of multiple happenings, etc. Journal of the Royal Statistical Society, 83, 255.

    Google Scholar 

  • Hodges, J. L., Krech, D. and Crutchfield, R. S. (1975) StatLab: An Empirical Introduction to Statistics. McGraw-Hill, New York.

    Google Scholar 

  • Jorgensen, B. (1987) Exponential dispersion models (with discussion). Journal of the Royal Statistical Society, B, 49, 127–162.

    Google Scholar 

  • Lindsey, J. K. (1974a) Comparison of probability distributions. Journal of the Royal Statistical Society, B, 36, 38–47.

    Google Scholar 

  • Lindsey, J. K. (1974b) Construction and comparison of statistical models. Journal of the Royal Statistical Society, B, 36, 418–425.

    Google Scholar 

  • Lindsey, J. K. (1992) Fitting distributions in GLIM as log-linear models. GLIM Newsletter 21, 9–12.

    Google Scholar 

  • Lindsey, J. K. and Mersch, G. (1992) Fitting and comparing probability distributions with log linear models. Computational Statistics and Data Analysis 13, 373–384.

    Google Scholar 

  • Spiegelhalter, D. J. and Smith, A. F. M. (1982) Bayes factors for linear and log-linear models with vague prior information. Journal of the Royal Statistical Society, B, 44, 377–387.

    Google Scholar 

  • Thyrion, P. (1961) Contribution à l'étude des bonus pour non sinistre en assurance automobile. ASTIN Bulletin, 1, 142–162.

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel

    Murray Aitkin

  2. Department of Mathematics, University of Western Australia, Nedlands, WA, Australia

    Murray Aitkin

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  1. Murray Aitkin
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Aitkin, M. Probability model choice in single samples from exponential families using Poisson log-linear modelling, and model comparison using Bayes and posterior Bayes factors. Stat Comput 5, 113–120 (1995). https://doi.org/10.1007/BF00143941

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