It is interesting to note that although Bayes' Theorem was named after Bayes himself, Bayes never published his original work. His colleagues Richard Price and Pierre Simon Laplace were the ones who contributed to the majority of his work and they were the ones who later made Bayes' work known to the public. Price extensively and rigorously edited Bayes’ work “An Essay Towards Solving a Problem in the Doctrine of Chances” (1763), which contains Bayes’ Theorem and is considered one of the fundamental results of probability theory. The French mathematician Pierre Simon Laplace (1749-1827) later extended Bayes’ work in his publication “Mémoire sur la probabilité des causes par les événements” (1774), which gave a clearer description of the inference problem for the unknown binomial parameter θ. Laplace was the one who finally established what would have been Bayes' Theorem.

There are endless applications to Bayes’ Theorem. The most widely used application in medicine is drug testing; for example, finding the probability that the person uses a drug given that he or she tests positive. Also, extensive studies have been devoted to investigating the probability of a patient dying from cancer given that he or she smokes. Another interesting application of Bayes’ Theorem is use in wartime. During World War II, Alan Turing used Bayes’ rule to guess the letters and crack the codes in the Enigma messages made by the Germans. Yet, Bayes’ Theorem could be used in the courtroom where the jurors might be interested in finding the probability of evidence given that the defendant is innocent. Also, in many cases, one may wish to find the probability that a defective item that he or she buys comes from certain companies that made the item in order to make better choices for future purchases.

There are endless applications to Bayes’ Theorem. The most widely used application in medicine is drug testing; for example, finding the probability that the person uses a drug given that he or she tests positive. Also, extensive studies have been devoted to investigating the probability of a patient dying from cancer given that he or she smokes. Another interesting application of Bayes’ Theorem is use in wartime. During World War II, Alan Turing used Bayes’ rule to guess the letters and crack the codes in the Enigma messages made by the Germans. Yet, Bayes’ Theorem could be used in the courtroom where the jurors might be interested in finding the probability of evidence given that the defendant is innocent. Also, in many cases, one may wish to find the probability that a defective item that he or she buys comes from certain companies that made the item in order to make better choices for future purchases.

Lola Argiro, Dayva Frank, Son Huynh, Wilhelmina (Nanrui) Tan