Bayesian epistemology

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Bayesian statistics
Posterior = Likelihood × Prior ÷ Evidence
Background
Bayesian inference Bayesian probability Bayes' theorem Bernstein–von Mises theorem Coherence Cox's theorem Cromwell's rule Likelihood principle Principle of indifference Principle of maximum entropy
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Posterior approximation
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Estimators
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Evidence approximation
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Model evaluation
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Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in Thomas Bayes' work in the field of probability theory.^[1] One advantage of its formal method in contrast to traditional epistemology is that its concepts and theorems can be defined with a high degree of precision. It is based on the idea that beliefs can be interpreted as subjective probabilities. As such, they are subject to the laws of probability theory, which act as the norms of rationality. These norms can be divided into static constraints, governing the rationality of beliefs at any moment, and dynamic constraints, governing how rational agents should change their beliefs upon receiving new evidence. The most characteristic Bayesian expression of these principles is found in the form of Dutch books, which illustrate irrationality in agents through a series of bets that lead to a loss for the agent no matter which of the probabilistic events occurs. Bayesians have applied these fundamental principles to various epistemological topics but Bayesianism does not cover all topics of traditional epistemology. The problem of confirmation in the philosophy of science, for example, can be approached through the Bayesian principle of conditionalization by holding that a piece of evidence confirms a theory if it raises the likelihood that this theory is true. Various proposals have been made to define the concept of coherence in terms of probability, usually in the sense that two propositions cohere if the probability of their conjunction is higher than if they were neutrally related to each other. The Bayesian approach has also been fruitful in the field of social epistemology, for example, concerning the problem of testimony or the problem of group belief. Bayesianism still faces various theoretical objections that have not been fully solved.