Bayes' Theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 31/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Bayes%27_theorem


00:01:28 1 Statement of theorem
00:03:32 2 Examples
00:03:41 2.1 Drug testing
00:06:51 2.2 A more complicated example
00:10:57 3 Interpretations
00:11:39 3.1 Bayesian interpretation
00:11:56 3.2 Frequentist interpretation
00:12:15 3.2.1 Example
00:13:15 4 Forms
00:14:05 4.1 Events
00:16:07 4.1.1 Simple form
00:16:16 4.1.2 Alternative form
00:16:24 4.1.3 Extended form
00:20:02 4.2 Random variables
00:22:16 4.2.1 Simple form
00:24:25 4.2.2 Extended form
00:24:42 4.3 Bayes' rule
00:24:52 5 Derivation
00:25:15 5.1 For events
00:27:41 5.2 For random variables
00:28:40 6 Correspondence to other mathematical frameworks
00:31:07 6.1 Propositional logic
00:31:16 6.2 Subjective logic
00:33:53 7 History
00:35:53 8 See also
00:36:04 9 Notes
00:39:57 10 Further reading
00:44:42 11 External links
00:46:22 See also
00:46:39 Notes
00:46:48 Further reading
00:50:05 External links



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SUMMARY
=======
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if cancer is related to age, then, using Bayes' theorem, a person's age can be used to more accurately assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person's age.
One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in Bayes' theorem may have different probability interpretations. With the Bayesian probability interpretation the theorem expresses how a subjective degree of belief should rationally change to account for availability of related evidence. Bayesian inference is fundamental to Bayesian statistics.
Bayes' theorem is named after Reverend Thomas Bayes (; 1701–1761), who first provided an equation that allows new evidence to update beliefs in his An Essay towards solving a Problem in the Doctrine of Chances (1763). It was further developed by Pierre-Simon Laplace, who first published the modern formulation in his 1812 "Théorie analytique des probabilités". Sir Harold Jeffreys put Bayes' algorithm and Laplace's formulation on an axiomatic basis. Jeffreys wrote that Bayes' theorem "is to the theory of probability what the Pythagorean theorem is to geometry".