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{{#invoke:sidebar|sidebar
{{ sidebar
| name = Bayesian statistics
| title = [[Bayesian statistics]]
| title = [[Bayesian statistics]]
| pretitle = Part of a series on
| image = [[File:Bayes icon.svg|80px]]
| image = [[File:Bayes icon.svg|80px]]
| class = hlist
| class = hlist


| heading1 =
| heading1 = Theory
| content1 =
| content1 = [[Posterior probability|Posterior]] = [[Likelihood function|Likelihood]] × [[Prior probability|Prior]] ÷ [[Marginal likelihood|Evidence]]

| heading2 = Background
| content2 = * [[Bayesian inference]]
* [[Bayesian probability]]
* [[Bayesian probability]]
* [[Probability interpretations]]
* [[Bayes' theorem]]
* [[Bayes' theorem]]
* [[Bayes' rule]]
* [[Bernstein–von Mises theorem]]
* [[Bayes factor]]
* [[Coherence (philosophical gambling strategy)|Coherence]]
* [[Cox's theorem]]
* [[Bayesian inference]]
* [[Cromwell's rule]]
* [[Bayesian network]]
* [[Prior probability|Prior]]
* [[Posterior probability|Posterior]]
* [[Likelihood function|Likelihood]]
* [[Conjugate prior]]
* [[Posterior predictive distribution|Posterior predictive]]
* [[Hyperparameter]]
* [[Hyperprior]]
* [[Principle of indifference]]
* [[Principle of indifference]]
* [[Principle of maximum entropy]]
* [[Principle of maximum entropy]]
* [[Empirical Bayes method]]
* [[Cromwell's rule]]
* [[Bernstein–von Mises theorem]]
* [[Bayesian information criterion]]
* [[Credible interval]]
* [[Maximum a posteriori estimation]]


| heading2 = Techniques
| heading3 = Model building
| content2 =
| content3 = * [[Uninformative prior|Weak prior]] ... [[Strong prior]]
* [[Conjugate prior]]
* [[Bayesian linear regression]]
* [[Bayesian linear regression|Linear regression]]
* [[Bayesian estimator]]
* [[Empirical Bayes method|Empirical Bayes]]
* [[Bayesian hierarchical modeling|Hierarchical model]]

| heading4 = Posterior approximation
| content4 =
* [[Markov chain Monte Carlo]]
* [[Laplace's approximation]]
* [[Integrated nested Laplace approximations]]
* [[Variational Bayesian methods|Variational inference]]
* [[Approximate Bayesian computation]]
* [[Approximate Bayesian computation]]


| heading5 = Estimators
| heading3 = Uses
| content3 =
| content5 = * [[Bayesian estimator]]
* [[Credible interval]]
* [[Bayesian spam filtering]]
* [[Binary classification]]
* [[Maximum a posteriori estimation]]
* [[Naive Bayes classifier]]


| heading6 = Evidence approximation
| content6 = * [[Evidence lower bound]]
* [[Nested sampling algorithm|Nested sampling]]

| heading7 = Model evaluation
| content7 = * [[Bayes factor]]
* [[Bayesian model averaging|Model averaging]]
* [[Posterior predictive distribution|Posterior predictive]]
| below =
| below =
}}
* {{Portal-inline|Mathematics}}
}}<noinclude>
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