THE BEGINNINGS OF PROBABILITY THEORY: BAYES’ SCARCE 1763 LANDMARK “ESSAY TOWARDS SOLVING A PROBLEM IN THE DOCTRINE OF CHANCES,” TOGETHER WITH HIS OFTEN-OVERLOOKED SECOND PAPER REGARDING PROBABILITY
BAYES, Thomas. An Essay towards Solving a Problem in the Doctrine of Chances. WITH: A Demonstration of the Second Rule in the Essay towards the Solution of a Problem in the Doctrine of Chances. IN: Philosophical Transactions, Vol. 53, pp. 370-418; and Vol. 54, pp. 296-325. London: L. Davis and C. Reymers, 1764-65. Two volumes. Quarto, contemporary marbled boards rebacked and recornered in calf, red morocco spine label, raised bands, uncut and largely unopened.
First editions of the first statement of Bayes’ theorem for calculating “inverse probabilities,” which forms the basis for methods of decision analysis, statistical learning machines, and Bayesian networks. Accompanying Bayes’ seminal, posthumous paper on probability is its lesser-known but important sequel, each as they originally appeared in Philosophical Transactions for 1763 and 1764, in the complete volumes for each year.
“Bayes’ Essay contains the first statement of Bayes’ Theorem for calculating ‘inverse probabilities,’ which forms the basis for methods of decision analysis, statistical learning machines, and Bayesian networks. Bayesian networks are complex diagrams that organize the body of knowledge in any given area by mapping out cause-and-effect relationships among key variables and encoding them with numbers that represent the extent to which one variable is likely to affect another. Programmed into computers, these systems can automatically generate optimal predictions or decisions even when key pieces of information are missing. Bayesian or subjective decision theory is arguably the most comprehensive theory of decision-making; however, until the late 1980s, it had little application due to the stupefying complexity of the mathematics involved. The rapid advances in computing power and the development of key mathematical equations during hte late 1980s and early 1990s made it possible to compute Bayesian networks with enough variables to be useful in practical applications” (Hook & Norman 1).
After Bayes’ death, his friend and fellow Nonconformist minister Richard Price presented these two papers, bequeathed to Price by Bayes, to the Philosophical Transactions of the Royal Society, along with his own completions and appendices. While the 1763 paper is well-known and its value widely recognized, the second paper from 1764 is often overlooked, probably due in part to the fact that Bayes’ name does not appear in the title nor in the Index for the volume. It is clear, however, that Price is presenting Bayes’ second paper, as he writes in his introduction that his own contribution consists only in “demonstrations of several propositions,” which “throw light on the nature of the curve by the quadrature”; on page 310 he writes “thus far I have transcribed Mr. Bayes.” In these two papers Bayes presents the basic lines of his theory which has solid ramifications in modern probability and statistics. In Bayes’ own words, “The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening” (Vol. 53, page 376). Bayes “found a rule for estimating the probability of future performance within certain bounds, given knowledge of the past record” (Norton History of Mathematical Sciences, 339-40). “Bayes is assured of his immortality: he was the first to use mathematical probability inductively” (Bell, The Development of Mathematics, 583). Each volume complete with a variety of interesting scientific papers on topics ranging from astronomy to mathematics to natural history to archaeology, a few accompanied by engraved plates, several folding. Ex-library Bristol Education Society, with early gift bookplate of Thomas Llewelyn, dated 1783, and a few discreet notations in red ink.
Text generally clean. Beautifully bound. A lovely uncut copy.