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Thomas Bayes

Thomas Bayes (1701 – 7 April 1761) was an English statistician, philosopher and Presbyterian minister, known for having formulated a specific case of the theorem that bears his name: Bayes' theorem.

Bayes' solution to a problem of inverse probability was presented in "An Essay towards solving a Problem in the Doctrine of Chances" which was read to the Royal Society in 1763 after Bayes' death. Richard Price shepherded the work through this presentation and its publication in the Philosophical Transactions of the Royal Society of London the following year. This was an argument for using a uniform prior distribution for a binomial parameter and not merely a general postulate. This essay contains a statement of a special case of Bayes' theorem.

Mathematically, Bayes' theorem gives the relationship between the probabilities of A and B, P(A) and P(B), and the conditional probabilities of A given B and B given A, P(A|B) and P(B|A). In its most common form, it is:

P(A/B) = P(B|A)P(A)/P(B)

Applications of Bayes' theorem

Bayes' Theorem is significantly important in inverse problem theory, where the a posteriori probability density function is obtained from the product of prior probability density function and the likelihood probability density function. An important application is constructing computational models of oil reservoirs given the observed data.

This theorem is effectively applied for any Big Data analytics, climate change predictions, economics, Stock buy or sell predictions also can be applied probability of terrorist attack and list goes on...