Bayes theorem or Bayes rule allows the estimation of the probability that, a hypothesis H is true when presented with a set of observations or evidence E. Let P(H) be the best estimate of the probability that hypothesis H is true prior to the availability of evidence E. Hence, P(H) is known as the prior probability of H. Let P(E|H) be the conditional probability (likelihood) of observing the evidence E given that, H is true and P(E) be the marginal probability of E. Then, the posterior probability of hypothesis H given evidence E is.
According to the Bayes rule, the posterior probability is proportional to the product of the likelihood and the prior probabilities.
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(2009). Bayes Rule. In: Li, S.Z., Jain, A. (eds) Encyclopedia of Biometrics. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-73003-5_747
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DOI: https://doi.org/10.1007/978-0-387-73003-5_747
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