Bayesian inference: An approach to the inference based largely on Bayes' Theorem and comprising of the below stated principal steps:
(1) Obtain the likelihood, f x q describing the process increasing the data x in terms of unknown parameters q.
(2) Obtain the previous distribution, f q expressing what is known about the q, previous to observing the data.
(3) Apply Bayes' theorem to derive posterior distribution f q x expressing that what is known about q after observing the given data.
(4) Derive suitable inference statements from posterior distribution. These might include speci?c inferences like interval estimates, point estimates or probabilities of the hypotheses or asumptions. If interest centres on particular components of q their posterior distribution is formed by the integrating out of the other parameters.
This form of inference varies from classical form of the frequentist inference in the various respects, particularly the use of prior distribution which is not present in the classical inference. It represents the investigator's knowledge and wisdom about the parameters before seeing data.
Classical statistics only makes use of the likelihood. As a result to the Bayesian every problem is unique and is considered by the investigator's beliefs about parameters expressed in the prior distribution for the speci?c or particular investigation.