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A form of reasoning that has received a great deal of attention from philosophers, mathematicians, and psychologists is based on theorems proposed by an 18th-century British cleric Thomas Bayes (1763) and the French astronomer and mathematician Pierre Laplace (1774). Today Bayes's name is more strongly associated with this development than is that of Laplace, who is better known for his work on celestial mechanics culminating in a five-volume opus by that title and his treatise on probability theory published in 1812; but Todhunter (1865/2001) credits Laplace with being the first to enunciate distinctly the principle for estimating the probability of causes from the observations of events. Although the popularity of Bayesian statistics waxed and waned—perhaps waned more than waxed—over the years, it has enjoyed something of a revival of interest among researchers during the recent past, as indicated by a near doubling of the annual number of published papers making use of it during the 1990s (Malakoff, 1999).
In classical logic, given the premise “If P, then Q, ” one cannot argue from the observation Q to the conclusion P; such an argument is known as “affirmation of the consequent” and is generally considered fallacious. Nevertheless