A Review of Bayesian Hypothesis Testing and Its Practical Implementations

We discuss hypothesis testing and compare different theories in light of observed or experimental data as fundamental endeavors in the sciences. Issues associated with the p-value approach and null hypothesis significance testing are reviewed, and the Bayesian alternative based on the Bayes factor is introduced, along with a review of computational methods and sensitivity related to prior distributions. We demonstrate how Bayesian testing can be practically implemented in several examples, such as the t-test, two-sample comparisons, linear mixed models, and Poisson mixed models by using existing software. Caveats and potential problems associated with Bayesian testing are also discussed. We aim to inform researchers in the many fields where Bayesian testing is not in common use of a well-developed alternative to null hypothesis significance testing and to demonstrate its standard implementation.

Automated summary

This article discusses the importance of hypothesis testing in the sciences and compares different theories based on observed or experimental data. It reviews the issues associated with the p-value approach and null hypothesis significance testing, introduces the Bayesian alternative based on the Bayes factor, and discusses computational methods and sensitivity related to prior distributions. The article demonstrates practical implementation of Bayesian testing in various examples and highlights potential caveats and problems associated with it.