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Bayes' theorem describes the inversion of probabilities. Let us consider two events and . Provided that , we have the following relationship between the conditional probabilities and :

(4.1)

Considering two random variables and with conditional distribution and marginal distribution ), the continuous version of Bayes' rule is as follows:

(4.2)

where is the prior distribution, is the posterior distribution, and is the likelihood function, which is also denoted by . This formula captures the essence of Bayesian statistical modeling, where denotes observations, and represents states or parameters. In order to build a Bayesian model, we need a parametric statistical model described by the likelihood function . Furthermore, we need to incorporate our knowledge about the system under study and the uncertainty about this information, which is represented by the prior distribution [44].