Bayesian refers to methods in probability and statistics named after Thomas Bayes (c. 1702–61), in particular methods related to statistical inference:
Bayesian probability or degree-of-belief interpretation of probability, as opposed to frequency or proportion or propensity interpretations
Bayes' theorem on conditional probability
Bayesian inference
These methods include:
Bayes estimator
Bayes factor
Bayesian average
Bayesian spam filtering
Bayesian game
Bayesian information criterion
Bayesian multivariate linear regression
Bayesian linear regression, a special case
Bayesian network
Empirical Bayes method
Naive Bayes classifier
Bayesian econometrics
Bayesian experimental design
Bayesian inference in phylogeny
Bayesian search theory
Bayesian vector autoregression
Bayesian also refers to the application of this probability theory to the functioning of the brain:
Bayesian approaches to brain function
Bayesian methods have been also applied to the interpretation of quantum mechanics:
Quantum Bayesianism