21 Facts About Bayesian inference


Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

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Bayesian inference is an important technique in statistics, and especially in mathematical statistics.

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Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law.

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Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data.

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Ian Hacking noted that traditional "Dutch book" arguments did not specify Bayesian inference updating: they left open the possibility that non-Bayesian inference updating rules could avoid Dutch books.

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The additional hypotheses needed to uniquely require Bayesian inference updating have been deemed to be substantial, complicated, and unsatisfactory.

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Decision-theoretic justification of the use of Bayesian inference was given by Abraham Wald, who proved that every unique Bayesian procedure is admissible.

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Wald characterized admissible procedures as Bayesian procedures, making the Bayesian formalism a central technique in such areas of frequentist inference as parameter estimation, hypothesis testing, and computing confidence intervals.

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Bayesian inference methodology plays a role in model selection where the aim is to select one model from a set of competing models that represents most closely the underlying process that generated the observed data.

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Bayesian inference has applications in artificial intelligence and expert systems.

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Bayesian inference techniques have been a fundamental part of computerized pattern recognition techniques since the late 1950s.

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Recently Bayesian inference has gained popularity among the phylogenetics community for these reasons; a number of applications allow many demographic and evolutionary parameters to be estimated simultaneously.

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Solomonoff's Inductive Bayesian inference is the theory of prediction based on observations; for example, predicting the next symbol based upon a given series of symbols.

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Bayesian inference has been applied in different Bioinformatics applications, including differential gene expression analysis.

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Bayesian inference is used in a general cancer risk model, called CIRI, where serial measurements are incorporated to update a Bayesian model which is primarily built from prior knowledge.

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Bayesian inference can be used by jurors to coherently accumulate the evidence for and against a defendant, and to see whether, in totality, it meets their personal threshold for 'beyond a reasonable doubt'.

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The benefit of a Bayesian inference approach is that it gives the juror an unbiased, rational mechanism for combining evidence.

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Bayesian inference argues that if the posterior probability of guilt is to be computed by Bayes' theorem, the prior probability of guilt must be known.

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Term Bayesian inference refers to Thomas Bayes, who proved that probabilistic limits could be placed on an unknown event.

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Early Bayesian inference, which used uniform priors following Laplace's principle of insufficient reason, was called "inverse probability".

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Nonetheless, Bayesian inference methods are widely accepted and used, such as for example in the field of machine learning.

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