Bayesian Statistics (Analysis)

Bayesian analysis is an approach to statistical analyses that is based on the Bayes's law, which states that the posterior probability of a parameter p is proportional to the prior probability of parameter p multiplied by the likelihood of p derived from the data collected. This increasingly popular methodology represents an alternative to the traditional (or frequentist probability) approach: whereas the latter attempts to establish confidence intervals around parameters, and/or falsify a-priori null-hypotheses, the Bayesian approach attempts to keep track of how a-priori expectations about some phenomenon of interest can be refined, and how observed data can be integrated with such a-priori beliefs, to arrive at updated posterior expectations about the phenomenon.

A good metaphor (and actual application) for the Bayesian approach is that of a physician who applies consecutive examinations to a patient so as to refine the certainty of a particular diagnosis: The results of each individual examination or test should be combined with the a-priori knowledge about the patient, and expectation that the respective diagnosis is correct. The goal is to arrive at a final diagnosis which the physician believes to be correct with a known degree of certainty.