The single-model approach to model selection based on
information criteria, such as AIC or BIC, is omnipresent in the
signal processing literature.
However, any single-model approach picks up only
one model and hence misses the potentially significant information
associated with the other models fitted to the data. In our opinion
this is a drawback:
indeed, depending on the application, even the true model structure
(assuming that there was one) may not be the best choice for the intended
use of the model. The multi-model approach does not suffer
from such a problem:
using nothing more than the values of AIC or BIC it estimates
the a posteriori probabilities of each model under consideration
and then it goes on to use all fitted models in a weighted manner
according to their posterior likelihoods. We show via a numerical
study that the multi-model approach can outperform the single-model
approach in terms of statistical accuracy, without unduly increasing
the computational burden. The first goal of this paper is to advocate
the multi-model approach. A second goal is to introduce some guidelines
for numerically studying the performance of a model selection rule.
2004. Vol. 14, no 5, 399-412 p.