Bayes' theorem
Contents
English[edit]
Alternative forms[edit]
Etymology[edit]
Named after English mathematician Thomas Bayes (1701–1761), who developed an early formulation. The modern expression of the theorem is due to Pierre-Simon Laplace, who extended Bayes' work but was apparently unaware of it.
Proper noun[edit]
- (probability theory) A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event.
- 2010, Jonathan Harrington, Phonetic Analysis of Speech Corpora, page 327,
- The starting point for many techniques in probabilistic classification is Bayes' theorem, which provides a way of relating evidence to a hypothesis.
- 2011, Allen Downey, Think Stats, O'Reilly, page 56,
- Bayes's theorem is a relationship between the conditional probabilities of two events.
- 2013, Norman Fenton, Martin Neil, Risk Assessment and Decision Analysis with Bayesian Networks, Taylor & Francis (CRC Press), page 131,
- We have now seen how Bayes' theorem enables us to correctly update a prior probability for some unknown event when we see evidence about the event.
- 2010, Jonathan Harrington, Phonetic Analysis of Speech Corpora, page 327,
Usage notes[edit]
The theorem is stated mathematically as:
- ,
where and are events with , and
- and are the marginal probabilities of observing and without regard to each other.
- The conditional probability is the probability of observing event given that is true.
- Similarly, is the probability of observing event given that is true.
Synonyms[edit]
- (theorem or equation describing conditional probability): Bayes' law, Bayes' rule
Related terms[edit]
See also[edit]
Further reading[edit]
- Bayesian inference on Wikipedia.Wikipedia
- Bayesian probability on Wikipedia.Wikipedia
- Bayesian statistics on Wikipedia.Wikipedia