This chapter introduces Bayesian methods, which are also called Bayesian algorithms, Bayesian machine learning, and probabilistic machine learning in the literature. We will first provide a general background for statistics-based machine learning, which contains statistical inference adopted by both frequentists and Bayesians. The frequentists’ inference method, i.e., maximum likelihood estimation, is used by many other machine learning methods like artificial neural networks, while Bayesians’ method, i.e., Bayesian estimation, is adopted as the basis of Bayesian methods in this chapter. Then, major parametric Bayesian methods, e.g., naive Bayes classifier, Bayesian networks, and Markov processes, will be discussed. Next, one nonparametric Bayesian method, i.e., Gaussian process, will be introduced.