Bayesian Model Comparison With the g-Prior

Model comparison and selection is an important
problem in many model-based signal processing applications.
Often, very simple information criteria such as the Akaike
information criterion or the Bayesian information criterion are
used despite their shortcomings. Compared to these methods,
Djuric’s asymptotic MAP rule was an improvement, and in this
paper we extend the work by Djuric in several ways. Specifically,
we consider the elicitation of proper prior distributions, treat
the case of real- and complex-valued data simultaneously in
a Bayesian framework similar to that considered by Djuric,
and develop new model selection rules for a regression model
containing both linear and non-linear parameters. Moreover,
we use this framework to give a new interpretation of the
popular information criteria and relate their performance to the
signal-to-noise ratio of the data. By use of simulations, we also
demonstrate that our proposed model comparison and selection
rules outperform the traditional information criteria both in
terms of detecting the true model and in terms of predicting
unobserved data. The simulation code is available online.