Abstract
In frequentist statistics, point-null hypothesis testing based on significance tests and confidence intervals are harmonious procedures and lead to the same conclusion. This is not the case in the domain of the Bayesian framework. An inference made about the point-null hypothesis using Bayes factor may lead to an opposite conclusion if it is based on the Bayesian credible interval. Bayesian suggestions to test point-nulls using credible intervals are misleading and should be dismissed. A null hypothesized value may be outside a credible interval but supported by Bayes factor (a Type I conflict), or contrariwise, the null value may be inside a credible interval but not supported by the Bayes factor (Type II conflict). Two computer programs in R have been developed that confirm the existence of a countable infinite number of cases, for which Bayes credible intervals are not compatible with Bayesian hypothesis testing.
DOI
10.22237/jmasm/1556670540
Recommended Citation
Lovric, M. M. (2019). Conflicts in Bayesian Statistics Between Inference Based on Credible Intervals and Bayes Factors. Journal of Modern Applied Statistical Methods, 18(1), eP3320. doi: 10.22237/jmasm/1556670540
Included in
Applied Statistics Commons, Social and Behavioral Sciences Commons, Statistical Theory Commons
