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This narrative review intends to provide the anesthesiologist with the basic knowledge of the Bayesian concepts and should be considered as a tutorial for anesthesiologists in the concept of Bayesian statistics. The Bayesian approach represents the mathematical formulation of the idea that we can update our initial belief about data with the evidence obtained from any kind of acquired data. It provides a theoretical framework and a statistical method to use pre-existing information within the context of new evidence. Several authors have described the Bayesian approach as capable of dealing with uncertainty in medical decision-making. This review describes the Bayes theorem and how it is used in clinical studies in anesthesia and critical care. It starts with a general introduction to the theorem and its related concepts of prior and posterior probabilities. Second, there is an explanation of the basic concepts of the Bayesian statistical inference. Last, a summary of the applicability of some of the Bayesian statistics in current literature is provided, such as Bayesian analysis of clinical trials and PKPD modeling., Author(s): Michele Introna [sup.1] [sup.2], Johannes P. van den Berg [sup.1], Douglas J. Eleveld [sup.1], Michel M. R. F. Struys [sup.1] [sup.3] Author Affiliations: (1) grid.4830.f, 0000 0004 0407 1981, [...]