Bayesian Method specifying hierarchical models for complex data by defining joint distributions of processes and parameters.

Bayesian refers to concepts and methods related to Bayesian probability and statistics, which are based on Bayes' theorem. This approach is named after the Reverend Thomas Bayes, an 18th-century mathematician and theologian who formulated a specific case of what is now called Bayes' theorem.
At its core, Bayes' theorem provides a way to update the probability of a hypothesis as more evidence or information becomes available. (such as rain tomorrow) or (such as a population mean), but Bayesian inference remained extremely difficult to implement until the late 1980s and early 1990s when powerful computers became widely accessible and new computational methods were developed, a concept were mathematically defined, which it's not).
Machine Learning: Bayesian methods are used in algorithms like Bayesian networks, Gaussian processes, and Bayesian neural networks.