This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing and machine learning. This article provides a comprehensive study of the state-of-the-art of the topic. We highlight limitations, benefits, connections and differences among the different techniques. Problems and possible solutions with the use of improper priors are also described. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments.
翻译:这是对用于模型选择和假设测试的边际可能性计算的最新介绍和概览。计算概率模型(或常数比率)的常数正常化是统计、应用数学、信号处理和机器学习等许多应用中的一个基本问题。本条款全面研究了这一专题的最新技术。我们强调不同技术的局限性、好处、联系和差异。还描述了使用不适当的前科的问题和可能的解决办法。通过理论比较和数字试验比较了一些最相关的方法。