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In Bayes’ theorem, an existing knowledge about the parameter(s) under investigation (the a priori distribution, or prior for short) is combined with the new knowledge from the data (‘likelihood’), resulting in a new, improved knowledge (a posteriori probability distribution).
An important benefit of Bayesian analysis is the ability to generate estimates and credible intervals for any derived parameter. Differences, ratios, effect sizes and novel parameter combinations are directly computed from the posterior distribution. Another benefit of Bayesian analysis is computationally robust estimates of parameter values and their credible intervals. The credible intervals do not depend on large-N approximations (as confidence intervals often do in frequentist approaches), nor do credible intervals depend on which tests are intended (as confidence intervals do in frequentist approaches). (Kruschke, John K., Bayesian Analysis Reporting Guidelines, Nature Human Behaviour, 2021)
