Bayes

Mathematical theorem and statistical method

 This article is about the theorem.
   For the surname, see Bayes (surname).

Thomas Bayes

Birth date	1701
Birth place	London, England
Died	7 April 1761
Place of death	Tunbridge Wells, England
Nationality	British
Known for	Bayes' theorem

Thomas Bayes (1701 – 7 April 1761) was an English statistician, philosopher, and Presbyterian minister. He is best known for Bayes' theorem, which describes the probability of an event based on prior knowledge of conditions that might be related to the event.

Early Life and Education

Thomas Bayes was born in London, England, in 1701. He was the son of a Presbyterian minister and followed in his father's footsteps by becoming a minister himself. Bayes studied at the University of Edinburgh, where he focused on logic and theology.

Bayes' Theorem

Main article: Bayes' theorem

Bayes' theorem is a fundamental result in probability theory that describes how to update the probabilities of hypotheses when given evidence. The theorem is expressed mathematically as: P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} where:

• P(A|B) is the probability of hypothesis A given the evidence B.
• P(B|A) is the probability of evidence B given that hypothesis A is true.
• P(A) is the probability of hypothesis A being true (prior probability).
• P(B) is the probability of the evidence (marginal likelihood).

Contributions to Statistics

Bayes' work laid the foundation for the field of Bayesian statistics, which is a subset of statistics in which probability expresses a degree of belief in an event. Bayesian statistics is widely used in various fields, including machine learning, data science, and artificial intelligence.

Legacy

Bayes' contributions to mathematics and statistics have had a lasting impact. His theorem is a cornerstone of modern statistical inference and has applications in a wide range of disciplines. The term "Bayesian" is used to describe methods and approaches that are based on Bayes' theorem.

Related Pages

• Bayesian statistics
• Probability theory
• Machine learning
• Data science
• Artificial intelligence
• University of Edinburgh

See Also

• Bayesian inference
• Bayesian network
• Frequentist probability
• Thomas Bayes

References

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