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 all the records and a stationary white Gaussian noise. To determine the correct model, the set of data records is partitioned into two disjoint subsets. One of the subsets is used for estimation of the model parameters and the remaining for validation of the model. Two proposed estimators for linear nested models are examined in detail and some of their properties derived. Optimal strategies for partitioning the data records into estimation and validation subsets are discussed and analytical comparisons with the information criterion A of Akaike (AIC) and the minimum description length (MDL) of Schwarz and Rissanen are carried out. The performance of the estimators and their comparisons with the AIC and MDL selection rules are illustrated by numerical simulations. The results show that the Bayesian selection rules outperform the popular AIC and MDL criteria.