MODEL SELECTION BASED ON BAYESIAN PREDICTIVE DENSITIES AND MULTIPLE DATA RECORDS

Bayesian predictive densities are used to derive model selection rules . The resulting rules hold for sets of data records where each record is composed of an unknown number of deterministic signals common to al l the records and a stationary white Gaussian noise. To determine the correct model, the set of data records is partitioned into two disjoin t subsets. One of the subsets is used for estimation of the model para meters and the remaining for validation of the model. Two proposed est imators for linear nested models are examined in detail and some of th eir properties derived. Optimal strategies for partitioning the data r ecords into estimation and validation subsets are discussed and analyt ical comparisons with the information criterion A of Akaike (AIC) and the minimum description length (MDL) of Schwarz and Rissanen are carri ed out. The performance of the estimators and their comparisons with t he AIC and MDL selection rules are illustrated by numerical simulation s. The results show that the Bayesian selection rules outperform the p opular AIC and MDL criteria.