Bayes' theorem

English Alternative forms en Bayes theorem en Bayes's theorem Etymology 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's work but was apparently unaware of it. Proper noun Bayes' theorem en probability theory A theorem expressed as an equation that describes the conditional probability of an event or state given prior knowledge of another event. en Bayes' law Bayes' rule en 2010 Jonathan Harrington Phonetic Analysis of Speech Corpora https://books.google.com.au/books?id=hHbR9O2YqE0C&pg=PA327&dq=%22Bayes%27+theorem%22&hl=en&sa=X&ved=0ahUKEwj6zMjtnK7WAhVpj1QKHS9AAxsQ6AEI-gIwOw#v=onepage&q=%22Bayes'%20theorem%22&f=false 327 The starting point for many techniques in probabilistic classification is Bayes' theorem, which provides a way of relating evidence to a hypothesis. en 2011 Allen Downey Think Stats https://books.google.com.au/books?id=TCfZ7d6skT4C&pg=PA56&dq=%22Bayes%27+theorem%22&hl=en&sa=X&ved=0ahUKEwj6zMjtnK7WAhVpj1QKHS9AAxsQ6AEIvAEwHA#v=onepage&q=%22Bayes'%20theorem%22&f=false 56 O'Reilly Bayes's theorem is a relationship between the conditional probabilities of two events. en 2013 Norman Fenton; Martin Neil Risk Assessment and Decision Analysis with Bayesian Networks Taylor & Francis (CRC Press) https://books.google.com.au/books?id=Wg7LBQAAQBAJ&pg=PA131&dq=%22Bayes%27+theorem%22&hl=en&sa=X&ved=0ahUKEwj6zMjtnK7WAhVpj1QKHS9AAxsQ6AEIigIwKA#v=onepage&q=%22Bayes'%20theorem%22&f=false 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. Usage notes The theorem is stated mathematically as: , where and are events with , and and are the en marginal probability marginal probabilities of observing and without regard to each other. The en conditional probability is the probability of observing event given that is true. Similarly, is the probability of observing event given that is true. Related terms en Bayesian See also en conditional probability Laplacean posterior probability prior#Noun<alt:priors>,posterior#Noun<alt:posteriors> prior probability Further reading Bayesian inference Bayesian probability Bayesian statistics en eponyms en Mathematics