Thomas Bayes (1701-1761), shown in the upper left, first discovered “Bayes’ theorem” in a paper that was published in 1764 three years after his death, as the name suggests. However, Bayes in his theorem used uniform priors [1]. Pierre-Simon Laplace (1749-1827), shown in the lower right, apparently unaware of Bayes’ work, discovered the same theorem in more general form in a memoir he wrote at the age of 25 and showed its wide applicability [2]. Regarding these issues S. M. Stiegler writes in [3] “The influence of this memoir was immense. It was from here that “Bayesian” ideas first spread through the mathematical world, as Bayes’s own article was ignored until 1780 and played no important role in scientific debate until the twentieth century. It was also this article of Laplace’s that introduced the mathematical techniques for the asymptotic analysis of posterior distributions that are still employed today. And it was here that the earliest example of optimum estimation can be found, the derivation and characterization of an estimator that minimized a particular measure of posterior expected loss. After more than two centuries, we mathematicians, statisticians cannot only recognize our roots in this masterpiece of our science, we can still learn from it.”

 

[1]          S. M. Stigler, “Thomas Bayes’s Inference”, J. Roy. Statistical Soc. A, vol. 145, pp. 250-258, 1982.

[2]          P. S. Laplace, “Mémoire sur la probabilité des causes par les événements”, Mémoires de mathématique et de physique presentés á l’Académie royale des sciences par divers savants & lus dans ses assemblées,  6, pp. 621-656, 1774.

[3]          S. M. Stigler, “Laplace’s 1774 Memoir on Inverse Probability”, Statistical Science, vol. 1, No. 3, pp. 359-363, 1986.