statistical inference Bayesian inference A statistical inference paradigm in which the assumptions are that parameters are random variables with probability distributions, that prior knowledge can be represented with such distributions, and that one learns from data by updating those prior distributions using Bayes' Rule. Harold Lehmann, Kenneth Wilkins SEVCO Philippe Rocca-Serra Regarding random variables with probability distribution: These random variables are often used to represent population parameters, but there are other types of random variables, e.g., representing typical methodological concerns, where the typical notion of “population” does not apply. Regarding prior knowledge: The notion of representing prior knowledge as a probability distribution is the core of disagreement among statisticians around Bayesian inference. For those interpreting “probability” as “measure of belief”, prior probability distributions encodes belief about the parameters (“subjectivist Bayes”), and ignorance is represented as a “non-informative” prior. For those with a more frequentist interpretation of probability, such priors summarizes frequency knowledge seen in the past (“empirical Bayes”). Regarding Bayes’ Rule: Probability theory, with no assumptions beyond regular probability, says that P(A|B) = P(B|A) P(A). Bayes Rule says that one can (should) use this formula to update knowledge from data: P(parameter value | data) = P(data | parameter value) P(Data), with P(data | parameter value) being called the “likelihood function,” communicating how likely data are, given parameter values (and what type of distribution the parameter(s) connote), and could be use to reflect sampling, if relevant. Bayesian approach ready for release