Marginal Likelihood Computation for Model Selection and Hypothesis Testing: An Extensive Review

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 ratios 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, bene-fits, 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.

Automated summary

This article provides an up-to-date introduction and overview of marginal likelihood computation for model selection and hypothesis testing. The computation of normalizing constants of probability models is a fundamental issue in various fields such as statistics, applied mathematics, signal processing, and machine learning. The article comprehensively discusses the state of the art in this area, including limitations, benefits, connections, and differences among different techniques. It also addresses problems and possible solutions related to the use of improper priors, and compares relevant methodologies through theoretical comparisons and numerical experiments.