Annals of the Institute of Statistical Mathematics

, Volume 32, Issue 1, pp 311-324

First online:

On the use of the predictive likelihood of a Gaussian model

  • Hirotugu Akaike

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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.