Hypothesis Testing Within Bayesian Inference

In a Bayesian framework, statistical inference relies on posterior distributions of unknown quantities and parameters of the models used for fitting data. From these, point estimators, credible intervals and posterior probabilistic statements can be produced. However, unlike the frequentist approach, hypothesis testing does not hold the same importance neither is a consensus matter between Bayesian statisticians, which regard the frequentist significance tests with reservation, admitting that they might serve a more complementary role to parameter estimation. Bayesian statistics, quite critics of p-values, suggests an investigation of the alternative hypotheses using the Bayes factor, only dependent on the observed data, for evaluating evidences in favour of the null hypothesis and being quite intuitive, forming a bridge to those interested in testing. Hypothesis tests have become completely essential in applied studies in areas such as biology, health and psychology, even though their generalized use is sometimes a problem, and the change in paradigm often stumbles in this particular difference between approaches. This work reviews the most common Bayesian approach for hypothesis testing, the Bayes factor, more robust and less demanding on assumptions and sample sizes than the frequentist approach, reflecting on its disadvantages, including sensitivity to prior distributions and computational difficulties, and misuses related to wrong interpretations. Two examples are detailed, including R code.