Bayesian refers to probability and statistics -- in particular:

• methods associated with the Reverend Thomas Bayes (ca. 1702–1761); or
• the degree-of-belief interpretation of probability, as opposed to frequency or proportion or propensity interpretations; or
• Bayes' theorem on conditional probability.

The development has taken place after his death, and includes:

• Bayesian probability
• Bayesian inference
• Bayesian network
• Bayes factor
• Bayesian model comparison
• Bayesian filtering
• Empirical Bayes method
• Naive Bayes classifier
• Bayesian game