  Any data modeling exercise has two main components: parameter estimation and
model selection. The latter will be the topic of this lecture note. More
concretely we will introduce several Monte-Carlo sampling-based rules for model
selection using the maximum a posteriori (MAP) approach. Model selection
problems are omnipresent in signal processing applications: examples include
selecting the order of an autoregressive predictor, the length of the impulse
response of a communication channel, the number of source signals impinging on
an array of sensors, the order of a polynomial trend, the number of components
of a NMR signal, and so on.
