Marginal likelihood computation for model selection and hypothesis testing: an extensive review. (arXiv:2005.08334v4 [stat.CO] UPDATED)

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. …

arxiv hypothesis review testing