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.

中文翻译：

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模型选择的蒙特卡洛抽样方法：入门 [讲义]

任何数据建模练习都有两个主要部分：参数估计和模型选择。后者将是本讲稿的主题。更具体地说，我们使用最大后验（MAP）方法引入了几个基于蒙特卡罗采样的模型选择规则。模型选择问题在信号处理应用中无处不在：示例包括选择自回归预测器的阶数、通信通道的脉冲响应长度、冲击传感器阵列的源信号的数量、多项式趋势的阶数、核磁共振信号的分量数量，等等。