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.

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

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

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.

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.

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

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.

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.

Bayesian inference has applications in artificial intelligence and expert systems.

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

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.

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.

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

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.

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'.

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

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.

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

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

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