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Bayes’ rule provides a decomposition of a conditional probability that is frequently used in a family of learning techniques collectively called Bayesian learning. Bayes’ rule is the equality
P(w) is called the prior probability, P(w | z) is called the posterior probability, and P(z | w) is called the likelihood.
Discussion
Bayes’ rule is used for two purposes. The first is Bayesian update. In this context z represents some new information that has become available since an estimate P(w) was formed of some hypothesis w. The application of Bayes’ rule enables a new estimate of the probability of w (the posterior probability) to be calculated from estimates of the prior probability, the likelihood, and P(z).
The second common application of Bayes’ rule is for estimating posterior probabilities in probabilistic learning, where it is the core of Bayesian networks, naïve Bayes, and semi-na...
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© 2016 Springer Science+Business Media New York
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Webb, G.I. (2016). Bayes’ Rule. In: Sammut, C., Webb, G. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7502-7_21-1
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DOI: https://doi.org/10.1007/978-1-4899-7502-7_21-1
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Publisher Name: Springer, Boston, MA
Online ISBN: 978-1-4899-7502-7
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Chapter history
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Latest
Bayes’ Rule- Published:
- 22 April 2023
DOI: https://doi.org/10.1007/978-1-4899-7502-7_21-2
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Original
Bayes’ Rule- Published:
- 12 August 2016
DOI: https://doi.org/10.1007/978-1-4899-7502-7_21-1