Bayes Theorem

"This is Bayes' Theorem. It is named after Rev. Thomas Bayes, an 18th century mathematician who derived a special case of this theorem. Bayes' calculations [2] were published in 1763, two years after his death. Exactly what Bayes intended to do with the calculation, if anything, still remains a mystery today. However, this theorem, as generalized by Laplace [3], is the basic starting point for inference problems using probability theory as logic." [1]

[1]

Bretthorst, G. Larry, "An Introduction to Model Selection Using Probability Theory as Logic", in Maximum Entropy and Bayesian Methods, Santa Barbara 1993, G. Heidbreder ed., Kluwer Academic Publishers, Dordrecht the Netherlands, 1994.

[2]

Bayes, Rev. T., "An Essay Toward Solving a Problem in the Doctrine of Chances", Philos. Trans. R. Soc. London 53, pp. 370-418 (1763); reprinted in Biometrika 45, pp. 293-315 (1958), and Two Papers by Bayes, with commentary by W. Edwards Deming, New York, Hafner, 1963.

[3]

Laplace, P. S., A Philosophical Essay on Probabilities, unabridged and unaltered reprint of Truscott and Emory translation, Dover Publications, Inc., New York, 1951, original publication date 1814.

Resources

Stutz, J., & Cheeseman, P., "A Short Exposition on Bayesian Inference and Probability"

Jaynes, E.T., "Probability Theory: The Logic of Science", 1994.

Press, S. James, "Bayesian Statistics: Principles, Models, and Applications", John Wiley & Sons, New York, 1989. [ The likeness of Rev. Bayes is from the frontispiece of this book. ]