Bayesian inference

Part of a series on
Bayesian statistics
Posterior = Likelihood × Prior ÷ Evidence
Background
  • Bayesian probability
  • Bayes' theorem
  • Bernstein–von Mises theorem
  • Coherence
  • Cox's theorem
  • Cromwell's rule
  • Likelihood principle
  • Principle of indifference
  • Principle of maximum entropy
Model building
  • Conjugate prior
  • Linear regression
  • Empirical Bayes
  • Hierarchical model
Posterior approximation
  • Markov chain Monte Carlo
  • Laplace's approximation
  • Integrated nested Laplace approximations
  • Variational inference
  • Approximate Bayesian computation
Estimators
Evidence approximation
  • Evidence lower bound
  • Nested sampling
Model evaluation
  • Bayes factor (Schwarz criterion)
  • Model averaging
  • Posterior predictive
  • Mathematics portal

Bayesian inference (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən)[1] is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability".

  1. ^ "Bayesian". Merriam-Webster.com Dictionary. Merriam-Webster.
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