Bayesian refers to methods in probability and statistics named after the Reverend Thomas Bayes (ca. 1702-1761), in particular methods related to:
Bayes's theorem Bayesian model comparison Bayesian linear regression Empirical Bayes method Bayesian information criterion Bayes factor Bayes estimator Naive Bayes classifier Thomas Bayes Bayesian network Bayesian spam filtering Bayesian game Bayesian probability Bayesian inference Probability Statistics