Annals of the Institute of Statistical Mathematics

, Volume 32, Issue 1, pp 311–324

On the use of the predictive likelihood of a Gaussian model

  • Hirotugu Akaike


The predictive likelihood of a model specified by data is defined when the model satisfies certain conditions. It reduces to the conventional definition when the model is specified independently of the data. The definition is applied to some Gaussian models and a method of handling the improper uniform prior distributions is obtained for the Bayesian modeling of a multi-model situation where the submodels may have different numbers of parameters. The practical utility of the method is checked by a Monte Carlo experiment of some quasi-Bayesian procedures realized by using the predictive likelihoods.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Akaike, H. (1977). On entropy maximization principle,Applications of Statistics (ed. P. R. Krishnaiah), North-Holland, Amsterdam, 27–41.Google Scholar
  2. [2]
    Akaike, H. (1978). A new look at the Bayes procedure,Biometrika,65, 53–59.MATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Akaike, H. (1979). A Bayesian extension of the minimum AIC procedure for autoregressive model fitting,Biometrika,66, 237–242.MATHMathSciNetCrossRefGoogle Scholar
  4. [4]
    Akaike, H., Kitagawa, G., Arahata, E. and Tada, F. (1979). TIMSAC-78,Computer Science Monographs, No. 11, The Institute of Statistical Mathematics, Tokyo.Google Scholar
  5. [5]
    Atkinson, A. C. (1978). Posterior probabilities for choosing a regression model,Biometrika,65, 39–48.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Atkinson, A. C. and Cox, David R. (1974). Planning experiments for discriminating between models, (with discussion),J. Roy. Statist. Soc., B,36, 321–348.MATHMathSciNetGoogle Scholar
  7. [7]
    Chow, Gregory C. (1979). A reconcilation of the information and posterior probability criteria for model selection,Research Memorandum No. 234, Econometric Research Program, Princeton University, revised, February, 1979.Google Scholar
  8. [8]
    Davis, W. W. (1979). Approximate Bayesian predictive distribution and model selection,J. Amer. Statist. Ass.,74, 312–317.MATHCrossRefGoogle Scholar
  9. [9]
    Dempster, Arther P. (1971). Model searching and estimation in the logic of inference,Foundation of Statistical Inference (eds. V. P. Godambe and D. A. Sprott), Holt, Rinehart and Winston of Canada, Toronto, 56–76.Google Scholar
  10. [10]
    Halpern, Elkan F. (1973). Polynomial regression from a Bayesian approach,J. Amer. Statist. Ass.,68, 137–143.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1980

Authors and Affiliations

  • Hirotugu Akaike

There are no affiliations available

Personalised recommendations