Bayesian analysis. Basic and practical concepts for its interpretation and use

Abstract

Bayesian statistics is based on subjective probability. It works with evidence updating considering the knowledge acquired prior to an investigation, plus the evidence obtained thereof. Results' interpretation requires for the hypotheses to be tested to be specified and their a priori probability to be estimated before the study. Study evidence is measured with the Bayes factor (compatibility ratio of the data under the proposed hypotheses). The conjunction of hypotheses a priori probabilities with the Bayes factor allows calculating the a posteriori probability of each one of them. The hypothesis with the highest degree of certainty at its update is the one that is accepted for decision making. In this review, three examples of hypothesis to be tested are shown: difference of means, correlation and association.