Abstract
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.
Similar content being viewed by others
References
Akaike, H. (1977). On entropy maximization principle,Applications of Statistics (ed. P. R. Krishnaiah), North-Holland, Amsterdam, 27–41.
Akaike, H. (1978). A new look at the Bayes procedure,Biometrika,65, 53–59.
Akaike, H. (1979). A Bayesian extension of the minimum AIC procedure for autoregressive model fitting,Biometrika,66, 237–242.
Akaike, H., Kitagawa, G., Arahata, E. and Tada, F. (1979). TIMSAC-78,Computer Science Monographs, No. 11, The Institute of Statistical Mathematics, Tokyo.
Atkinson, A. C. (1978). Posterior probabilities for choosing a regression model,Biometrika,65, 39–48.
Atkinson, A. C. and Cox, David R. (1974). Planning experiments for discriminating between models, (with discussion),J. Roy. Statist. Soc., B,36, 321–348.
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.
Davis, W. W. (1979). Approximate Bayesian predictive distribution and model selection,J. Amer. Statist. Ass.,74, 312–317.
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.
Halpern, Elkan F. (1973). Polynomial regression from a Bayesian approach,J. Amer. Statist. Ass.,68, 137–143.
Additional information
The Institute of Statistical Mathematics
About this article
Cite this article
Akaike, H. On the use of the predictive likelihood of a Gaussian model. Ann Inst Stat Math 32, 311–324 (1980). https://doi.org/10.1007/BF02480336
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02480336