Monte-Carlo Sampling Approach to Model Selection: A Primer

TL;DR

This paper introduces Monte-Carlo sampling methods for model selection within the MAP framework, addressing common problems in signal processing such as choosing model order and component number.

Contribution

It presents several Monte-Carlo sampling-based rules specifically designed for model selection using the MAP approach, providing practical tools for signal processing applications.

Findings

Monte-Carlo sampling rules for model selection are effective.

Applicable to various signal processing problems.

Enhances model selection accuracy with sampling techniques.

Abstract

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.