When we speak of Bayesianism, we are referring to a philosophical and statistical framework that involves the representation of degrees of belief or justification using probabilities. It is characterized by the idea that belief comes in degrees that can be formalized using the axioms of probability theory. Bayesianism involves the assessment of the rationality of degrees of belief based on a set of rules and specifies how these beliefs can be updated using Bayes' theorem based on new information or evidence.

Many statistics textbooks treat frequentist statistics as the main subject and relegate Bayesian statistics to a single chapter, often near the end of the book.

The idea of this Special Issue of Entropy has been to treat Bayesian statistics as the main topic and to provide a snapshot of how Bayesian inference is understood and how it contributes to scientific endeavor today, late in the first quarter of the 21st Century.

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