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Bayesian Statistics

  Bayes\'s rule, formulated by Thomas Bayes (1702 - 1761) sparked off a radical new direction in statistics, the application in mathematics of probability theory. The rule shows how to handle ‘conditional probabilities’, ones which show the effect of one event on another. For example, the probability that a patient has back trouble is higher if it is known that he or she claims to have back pains. We make one event (that the patient claims to have back pains) a condition of the other (that he or she has back trouble). It is usual to write the conditional probability of event A given that event B is known to have happened as p(A B); Bayes\'s rule tells us that p(A) = p(A B) × p(B) + p(A not B) × p(not B).

Bayes\'s rule is used to find the probability of an event experimentally; the experimenter starts off with a degree of belief in each of his or her hypotheses, and uses Bayes\'s rule to modify these degrees of belief according to the results of experimentation (for example, an experiment could consist of asking a patient if he or she has back pains). The method is commonly used today by computers, providing ‘expert systems’ used in medicine, prospecting and fault diagnosis. SMcL



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