List of Important Publications in Statistics - Bayesian Statistics

Bayesian Statistics

An Essay towards solving a Problem in the Doctrine of Chances

Author: Thomas Bayes

Publication data: 1763-12-23

Online version: "An Essay towards solving a Problem in the Doctrine of Chances. By the late Rev. Mr. Bayes, F.R.S. communicated by Mr. Price, in a Letter to John Canton, A.M. F.R.S." (pdf). Department of Mathematics, University of York. http://www.york.ac.uk/depts/maths/histstat/essay.pdf.

Description: In this paper Bayes addresses the problem of using a sequence of identical "trials" to determine the per-trial probability of "success" — the so-called inverse probability problem. It later inspired the theorem that bears his name (Bayes' theorem). See also Pierre Simon de Laplace.

Importance: Topic creator, Breakthrough, Influence

On Small Differences in Sensation

Author: Charles Sanders Peirce and Joseph Jastrow

Publication data: Peirce, Charles Sanders; Jastrow, Joseph (1885). "On Small Differences in Sensation". Memoirs of the National Academy of Sciences 3: 73–83. http://psychclassics.yorku.ca/Peirce/small-diffs.htm.

Online version: http://psychclassics.yorku.ca/Peirce/small-diffs.htm

Description: Peirce and Jastrow use logistic regression to estimate subjective probabilities of subjects's judgments of the heavier of two measurements, following a randomized controlled repeated measures design.

Importance: Pioneered elicitation of subjective probabilities.

Truth and Probability

Author: Frank P. Ramsey

Publication data: * Ramsey, Frank Plumpton; “Truth and Probability” (PDF), Chapter VII in The Foundations of Mathematics and other Logical Essays (1931).

Online version: http://cepa.newschool.edu/het//texts/ramsey/ramsess.pdf

Description: Ramsey proposes elucidating a person's subjective probability for a proposition using a sequence of bets. Ramsey described his work as an elaboration of some pragmatic ideas of C. S. Peirce, which were expressed in "How to Make Our Ideas Clear".

Importance: Popularized the "Ramsey test" for eliciting subjective probabilities.

Probability, Induction and Statistics

Author: Bruno de Finetti

Publication data: New York: John Wiley & Sons, Inc., 1972.

Description A collection of de Finetti's essays on subjective probability.

Importance: Proved de Finetti's theorem on the representation of an infinite sequence of exchangeable random variables by a mixture of independent random variables.

Theory of Probability

Author: Bruno de Finetti

Publication data: Two volumes, A.F.M. Smith and A. Machi (trs.), New York: John Wiley & Sons, Inc., 1974, 1975.

Description The first detailed statement of the operational subjective position, dating from the author's research in the 1920s and 30s.

Importance: Emphasizes exchangeable random variables which are often mixtures of independent random variables. Argues for finitely additive probability measures that need not be countably additive. Emphasizes expectations rather than probability measures.

Introduction to statistical decision theory

Author: John W. Pratt, Howard Raiffa, and Robert Schlaifer

Publication data: preliminary edition, 1965. Cambridge, Mass.: MIT Press, 1995.

Description Extensive exposition of statistical decision theory, statistics, and decision analysis from a Bayesian standpoint. Many examples and problems come from business and economics.

Importance: Greatly extended the scope of applied Bayesian statistics by using conjugate priors for exponential families. Extensive treatment of sequential decision making, for example mining decisions. For many years, it was required for all doctoral students at Harvard Business School.