Bayes’ Theorem or Bayes’ Law or Bayes’ rule is used to express the conditional probability or posterior probability of a hypothesis H in terms of prior probability of H. It is based on the concept of that evidence effects if it more likely given H than not –H. It is generally applied in engineering and sciences and is valid in all usual interpretations of probability.
Bayes’ theorem was discovered by the Reverend Thomas Bayes in 17th century during his study on computation of a distribution for the probability parameter of a binomial distribution. His work was edited and published by his friend Richard Price after his death in 1763 with the title of An Essay towards solving a Problem in the Doctrine of Chances.
In Bayes’ theorem we define each probability with a name as:
P(A) is described as the prior probability of A
P(A|B) is known as conditional probability of A given B or posterior probability
P (B|A) is also known as likelihood and is the conditional probability of B given A.
P(B) is defined as prior or marginal probability of B
Mostly Bayes’ theorem is used in various fields of research work such as drug testing and Bayesian inference. Presently Bayes’ Theorem of Bayes’ Law is used to computer various variables as well as is used to reject the idea of the God’s presence.