Marginal likelihood computation for model selection and hypothesis testing: an extensive review Articles uri icon

publication date

  • January 2023

start page

  • 3

end page

  • 58


  • 65

International Standard Serial Number (ISSN)

  • 0036-1445

Electronic International Standard Serial Number (EISSN)

  • 1095-7200


  • 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, 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.


  • marginal likelihood; bayesian evidence; numerical integration; model selection; hypothesis; testing; quadrature rules; doubly intractable posteriors; partition functions