Bayesian statistics in a branch of statistics that emphasizes subjective probability as opposed to objective probabilities (frequentists). While both subjectivists and frequentists rely on data, the latter eschew the notion of prior expectation in the computation of probability after experiments or data analysis (in general). Furthermore, there are fundamental philosophical differences between the two branches that cannot be summarized in a few key words or phrases. Bayesian statistics emerged from the work of Thomas Bayes (1763) and the ongoing work of many statisticians and programmers who brought the basis of Bayes Theorem to modern computing platforms. Many books focus on the nature of Bayesian statistics so this answer will not go into great depth but rather refer interested readers to several more elaborate answers: