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 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 nuclear magnetic resonance signal, and so on.