Bayesian Analysis

When did Bayesian inference become "Bayesian"?

Stephen E. Fienberg

Full-text: Open access

Abstract

While Bayes' theorem has a 250-year history, and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective "Bayesian" was not part of the statistical lexicon until relatively recently. This paper provides an overview of key Bayesian developments, beginning with Bayes' posthumously published 1763 paper and continuing up through approximately 1970, including the period of time when "Bayesian" emerged as the label of choice for those who advocated Bayesian methods.

Article information

Source
Bayesian Anal. Volume 1, Number 1 (2006), 1-40.

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
http://projecteuclid.org/euclid.ba/1340371071

Digital Object Identifier
doi:10.1214/06-BA101

Mathematical Reviews number (MathSciNet)
MR2227361

Citation

Fienberg, Stephen E. When did Bayesian inference become "Bayesian"?. Bayesian Anal. 1 (2006), no. 1, 1--40. doi:10.1214/06-BA101. http://projecteuclid.org/euclid.ba/1340371071.


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References

  • Aldrich, J. (1997). "R.A. Fisher and the Making of Maximum Likelihood 1912–1922." Statistical Science, 12: 162–176.
  • –- (2002). "How Likelihood and Identification Went Bayesian." International Statistical Review, 70.
  • Anscombe, F. J. (1961). "Bayesian Statistics." American Statistician, 15: 21–24.
  • Anscombe, F. J. and Aumann, R. J. (1963). "A Definition of Subjective Probability." Annals of Mathematical Statistics, 34: 199–205.
  • Arrow, K. J., Girshick, M. A., and Rubin, H. (1949). "`Bayes and Minimax Solutions of Sequential Decision Problems." Econometrica, 17: 213–244.
  • Association, A. S. (2003). "David Blackwell. Go Bayes!" Amstat News, 6–7.
  • Bailey, A. L. (1950). "Credibility Procedures, Laplace's Generalization of Bayes' Rule and the Combination of Collateral Knowledge with Observed Data." In Proceedings of the Casualty Actuarial Society, volume 37, 7–23.
  • Banks, D. L. (1996). "A Conversation with I.J. Good." Statistical Science, 11: 1–19.
  • Barnard, G. A. (1946). "Sequential Tests in Industrial Statistics." Supplement to the Journal of the Royal Statistical Society, 8: 1–26.
  • –- (1972). "The Unity of Statistics." Journal of the Royal Statistical Society, Series A, 135: 1–15.
  • –- (1987). "R. A. Fisher–-A True Bayesian?" International Statistical Review, 55: 183–189.
  • Barnard, G. A. and Plackett, R. L. (1985). "Statistics in the United Kingdom, 1939–45." In Atkinson, A. C. and Fienberg, S. E. (eds.), A Celebration of Statistics: The ISI Centenary Volume, 31–56. New York: Springer-Verlag.
  • Barnett, V. (1973). Comparative Statistical Inference. Wiley.
  • Bayes, T. (1763). "An Essay Towards Solving a Problem in the Doctrine of Chances." Philosophical Transactions of the Royal Society of London, 53: 370–418.
  • Bellhouse, D. R. (2002). "On Some Recently Discovered Manuscripts of Thomas Bayes." Historia Mathematica, 29: 383–394.
  • –- (2004). "The Reverend Thomas Bayes FRS": A Biography to Celebrate the Tercentenary of his Birth (with discussion). Statistical Science, 3–43.
  • Bienaymé, I. (1838). "Mémoire sur la Probabilité des Résultats Moyens des Observations; Démonstration Directe de la Règle de Laplace." Mém. Pres. Acad. Roy. Sci. Inst. France, 5: 513–558.
  • Birnbaum, A. (1962). "On the Foundations of Statistical Inference (with discussion)." Journal of the American Statistical Association, 57: 269–326.
  • Blackwell, D. and Girshick, M. A. (1954). Theory of Games and Statistical Decisions. Wiley.
  • Borel, E. (1921). "La Théorie du Jeu et les Équations Intégrales à Noyau Symétrique." Comptes Rendus de l'Académie des Sciences, 173: 1304–1308. Translated by L. J. Savage as “The Theory of Play and Integral Equations with Skew Symmetric Kernels." Econometrica, 21, 97–100.
  • –- (1924). "À Propos d'un Traité de Probabilités." Revue Philosophique, 98: 321–336. Translated as “A Propos of a Treatise on Probability." In Kyburg, H. E. and Smokler, H. E., eds. (1964). Studies in Subjective Probability. Wiley, New York, 45–60.
  • –- (1924). "Sur lex Jeux où Interviennent L'hasard et L'habileté des Joueurs." In Théorie des Probabilités, 204–224. Librairie Scientifique, J. Herman.
  • –- (1927). "Sur les Systèmes de Formes Linéaires à Déterminant Symétrique Gauche et la Théorie Génerale du Jeu. from Algèbre et Calcul des Probabilités." Comptes Rendus de l'Académie des Sciences, 173: 52–53.
  • Box, G. E. P. and Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. Holden-Day.
  • Box, G. E. P. and Tiao, G. C. (1961). "A Further Look at Robustness Via Bayes' Theorem." Biometrika, 49: 419–432.
  • –- (1973). Bayesian Inference in Statistical Analysis. Addison-Wesley.
  • Brillinger, D. A. (2002). "John W. Tukey: His Life and Professional Contributions." Annals of Statistics, 30: 1535–1575.
  • Broemeling, L. and Broemeling, A. (2003). "Studies in the History of Probability and Statistics: XLVIII". The Bayesian Contributions of Ernest Lhoste. Biometrika, 90: 728–731.
  • Carnap, R. (1950). Logical Foundations of Probability. University of Chicago Press.
  • Chernoff, H. (1954). "Rational Selection of Decision Functions." Econometrica, 22: 422–443.
  • Christ, C. F. (1994). "The Cowles Commission's Contributions to Econometrics at Chicago, 1939-1955." Journal of Economic Literature, 32: 30–59.
  • Christensen, R. and Johnson, W. (2004). "Conversation with Seymour Geisser." Statistical Science.
  • Condorcet, M.-J.-A.-N. d. C. (1785). Essai sur L'application de L'analyse à la Probabilité des Décisions Rendues à la Pluraltté des Voix. Imprimerie Royale.
  • Cornfield, J. (1969). "The Bayesian Outlook and Its Application (with discussion)." Biometrics, 25: 617–657.
  • Cournot, A. A. (1984). Exposition de la Theorie des Chances et des Probabilités.. Librairie J. Vrin.
  • Dale, A. I. (1999). A History of Inverse Probability from Thomas Bayes to Karl Pearson. Springer-Verlag.
  • –- (2003). Most Honourable Remembrance: The Life and Work of Thomas Bayes. Springer-Verlag.
  • Daston, L. (1994). "How Probabilities Came to be Objective and Subjective." Historia Mathematica, 21: 330–344.
  • David, H. A. (1995). "First (?) Occurrence of Common Terms in Mathematical Statistics." American Statistician, 49: 121–133.
  • –- (1998). "First (?) Occurrence of Common Terms in Probability and Statistics – A Second List, with Corrections." American Statistician, 52: 36–40.
  • –- (2001). "Appendix B." In David, H. A. and Edwards, A. W. F. (eds.), Annotated Readings in the History of Statistics. Springer-Verlag.
  • de Finetti, B. (1937). "La Prévision: Ses Lois Logiques, Ses Sources Subjectives." Annales de l'Institut Henri Poincaré, 7: 1–68. Translated as “Foresight: Its Logical Laws, Its Subjective Sources," in Kyburg, H. E. and Smokler, H. E. eds., (1964). Studies in Subjective Probability. Wiley, New York, 91–158. (Corrections appear in (de Finetti, 1972, p. xvii)).
  • –- (1951). "Recent Suggestions for the Reconciliation of Theories of Probability." In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, volume 1, 217–225. Berkeley: University of California Press.
  • –- (1955). "La Notion de `Horizon Bayesien.'." In Thone, G. (ed.), Colloque Sur l'Analyse Statistique, Bruxelles, 57–71. Paris: Liège and Masson & Cie.
  • –- (1974). Theory of Probability, volume I. Wiley.
  • –- (1975). Theory of Probability, volume II. Wiley.
  • De Morgan, A. (1837). "Review of Laplace's Théorie Analytique des Probabilités. (3rd Edition)." Dublin Review, 2, 3: 338–354, 237–248.
  • DeGroot, M. A. (1970). Optimal Statistical Decisions. McGraw-Hill.
  • Edgeworth, F. Y. (1883). "The Method of Least Squares." Philosophical Magazine, 5th series, 34: 190–204.
  • Edwards, A. W. F. (1997). "What Did Fisher Mean by `Inverse Probability' in 1912–1922?" Statistical Science, 12: 177–184.
  • –- (2004). "Comment on Bellhouse, David R. `The Reverend Thomas Bayes FRS: A Biography to Celebrate the Tercentenary of his Birth'." Statistical Science, 19: 34–37.
  • Edwards, W., Lindman, H., and Savage, L. J. (1963). "Bayesian Statistical Inference for Psychological Research." Psychological Review, 70: 193–242.
  • Efron, B. (2005). "Bayesians, Frequentists, and Scientists." Journal of the American Statistical Association, 100.
  • Efron, B. and Morris, C. (1973). "Stein's Estimation Rule and its Competitors–-An Empirical Bayes Approach." Journal of the American Statistical Association, 68: 117–130.
  • Fechner, G. T. (1897). Kollektivmasslehre. Engelmann.
  • Fienberg, S. E. (1985). "Statistics Developments in World War II": An International Perspective. In Atkinson, A. C. and Fienberg, S. E. (eds.), A Celebration of Statistics: The ISI Centenary Volume, 25–30. Springer-Verlag.
  • –- (1992). "A Brief History of Statistics in Three and One-half Chapters: A Review Essay." Statistical Science, 7: 208–225.
  • –- (1999). "`Statistics in the Social World,' a review of The Politics of Large Numbers: A History of Statistical Reasoning, by Alain Desrosières." Science, 283: 2025.
  • –- (2005). "Interview with Howard Raiffa." Statistical Science.
  • Fienberg, S. E. and Lazar, N. (2001). "William Sealy Gosset: 1876-1937." In Heyde, C. and Seneta, E. (eds.), Statisticians of the Centuries. New York: Springer-Verlag.
  • Fienberg, S. E. and Tanur, J. M. (1996). "Reconsidering the Fundamental Contributions of Fisher and Neyman on Experimentation and Sampling." International Statistical Review, 64: 237–253.
  • Fisher, R. A. (1922). "On the Mathematical Foundations of Theoretical Statistics." Philosophical Transactions of the Royal Society of London, Series A, 222: 309–368.
  • –- (1925). Statistical Methods for Research Workers. Oliver and Boyd.
  • –- (1930). "`Inverse Probability." Proceedings of the Cambridge Philosophical Society, 26: 528–535.
  • –- (1950). Contributions to Mathematical Statistics. Wiley.
  • –- (1956). Statistical Methods and Scientific Inference. Oliver and Boyd.
  • Fraser, D. A. S. (1968). The Structure of Inference. Wiley.
  • Geisser, S. and Cornfield, J. (1963). "Posterior Distributions for Multivariate Normal Parameters." Journal of the Royal Statistical Society, Series B, 25: 368–376.
  • Gigerenzer, G., Swijtink, Z., Porter, T., Daston, L., Beatty, J., and Krüger, L. (1989). The Empire of Chance: How Probability Changed Everyday Life. Cambridge University Press.
  • Girshick, M. A. and Rubin, H. (1952). "A Bayes Approach to a Quality Control Model." Annals of Mathematical Statistics, 23: 114–125.
  • Good, I. (1950). Probability and the Weighing of Evidence. Charles Griffin.
  • –- (1979). "Studies in the History of Probability and Statistics: XXXVII". Turing's Statistical Work in World War II. Biometrika, 66: 393–396.
  • Good, I. J. (1952). "Rational Decisions." Journal of the Royal Statistical Society, Series B, 14: 107–114.
  • –- (1953). "The Population Frequencies of Species and the Estimation of Population Parameters." Biometrika, 40: 237–264.
  • –- (1956). "Review of B. de Finetti (1954)." Mathematical Reviews, 17: 633.
  • –- (1958). "Significance Tests in Parallel and in Series." Journal of the American Statistical Association, 53: 799–813.
  • –- (1965). The Estimation of Probabilities. The M.I.T. Press.
  • –- (1976). "The Bayesian Influence, or How to Sweep Subjectivism Under the Carpet." In Hooker, C. A. and Harper, W. (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, volume 2, 125–174. Dordrecht, Holland: D. Reidel.
  • –- (1983). Good Thinking: The Foundations of Probability and its Applications. University of Minnesota Press.
  • –- (1992). "Introduction to Robbins (1955), An Empirical Bayes Approach to Statistics." In Johnson, N. L. and Kotz, S. (eds.), Breakthroughs in Statistics, Vol. I: Foundations and Basic Theory, 379–387. Springer-Verlag. This is in fact an introduction to Robbin's 1956 paper [Robbins:1956?].
  • Good, I. J. and Toulmin, G. (1956). "The Number of New Species, and the Increase in Population Coverage, When a Sample is Increased." Biometrika, 43: 45–63.
  • Hald, A. (1998). A History of Mathematical Statistics From 1750 to 1930. Wiley.
  • Heyde, C. C. and E., S. (1977). I. J. Bienaymé: Statistical Theory Anticipated. Springer-Verlag.
  • –- (2001). Statisticians of the Centuries. Springer-Verlag.
  • Howie, D. (2002). Interpreting Probability: Controversies and Developments in the Early Twentieth Century. Cambridge University Press.
  • Jeffreys, H. (1931). Scientific Inference. Cambridge University Press.
  • –- (1939). Theory of Probability. Oxford University Press.
  • Kadane, J. B. (2001). "Jimmie Savage: An Introduction." ISBA Bulletin, 8: 5–6.
  • Kapteyn, J. C. (1903). Skew Frequency Curves in Biology and Statistics. Noordhoff.
  • Kasner, E. and Newman, J. R. (1940). Mathematics and the Imagination. Simon and Schuster.
  • Keynes, J. M. (1921). A Treatise on Probability, volume 8. St Martin's.
  • Kolmogorov, A. (1933). "`Sur Léstimation Statisque des Parametres de la Loi de Gauss." Bulletin of the Academy of Science URSS Ser. Math., 6: 3–32.
  • Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer-Verlag.
  • Kyburg, H. E. and Smokler, H. E. (eds.) (1964). Studies in Subjective Probability. New York: Wiley. Second revised edition, Krieger, Garden City, 1980.
  • Lacroix, S. F. (1816). "Traité É\'le"mentaire du Calcul des Probabilités.
  • Laplace, P.-S. (1774). "`Mémoire sur la Probabilité des Causes par les Événements." Mémoires de Mathématique et de Physique Presentés á l'Académie Royale des Sciences, Par Divers Savans, & Lûs dans ses Assemblées, 6: 621–656.
  • –- (1812). Théorie Analytique des Probabilités. Courcier.
  • Lévy, P. (1925). Calcul de Probabilités. Gauthier-Villars.
  • Lhoste, E. (1923). "Le Calcul des Probabilités Appliqué a L'artillerie." Revue D'artillerie, 91, 92: 405–423 and 516–532, 58–82 and 152–179.
  • Lindley, D. V. (1953). "Statistical Inference." Journal of the Royal Statistical Society, Series B, 16: 30–76.
  • –- (1957). "Fiducial Distributions and Bayes' Theorem." Journal of the Royal Statistical Society, Series B, 20: 102–107.
  • –- (1957). "A Statistical Paradox." Biometrika, 44: 187–192.
  • –- (1958). "Fiducial Distributions and Bayes' Theorem." Journal of the Royal Statistical Society, Series B, 20: 102–107.
  • –- (1958). "Professor Hogben's `Crisis'–A Survey of the Foundations of Statistics." Applied Statistics, 7: 186–198.
  • –- (1965). Introduction to Probability and Statistics from a Bayesian Viewpoint. Part 1: Probability. Part 2: Inference. Cambridge University Press.
  • –- (2000). "What is a Bayesian?" ISBA Bulletin, 1: 7–9.
  • –- (2004). "Bayesian Thoughts (An Interview with Helen Joyce)." Significance, 1: 73–75.
  • –- (2004). "That Wretched Prior." Significance, 1: 85–87.
  • Lindley, D. V. and Smith, A. F. M. (1972). "Bayes Estimates for the Linear Model (with discussion)." Journal of the Royal Statistical Society, Series B, 34: 1–44.
  • Luce, D. and Raiffa, H. (1957). Games and Decisions: Introduction and Critical Survey. Wiley.
  • Mayerson, A. L. (1964). "A Bayesian View of Credibility." Proceedings of the Casualty Actuarial Society, 51: 85–104.
  • Metropolis, N. (1987). "The Beginning of the Monte Carlo Method." Los Alamos Science, 125–130.
  • Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). "Equations of State Calculations by Fast Computing Machines." Journal of Chemical Physics, 21: 1087–1092.
  • Metropolis, N. and Ulam, S. (1949). "The Monte Carlo Method." Journal of the American Statistical Association, 44: 335–341.
  • Mosteller, F. (1948). "On Pooling Data." Journal of the American Statistical Association, 43: 231–242.
  • Mosteller, F. and Nogee, P. (1951). "An Experimental Measurement of Utility." Journal of Political Economy, 59: 371–404.
  • Mosteller, F. and Wallace, D. L. (1963). "Inference in an Authorship Problem." Journal of the American Statistical Association, 58: 275–309.
  • –- (1964). Inference and Disputed Authorship: The Federalist. Addison-Wesley.
  • Nagel, E. (1936). "The Meaning of Probability (with discussion)." Journal of the American Statistical Association, 31: 10–30.
  • –- (1938). The Principles of the Theory of Probability. University of Chicago Press.
  • Neyman, J. (1937). "Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability." Philosophical Transactions of the Royal Society, Series A, 236: 333–380.
  • of Mathematical Statistics, I. (1988). "The Reverend Thomas Bayes, F.R.S."–-1701?-1761. IMS Bulletin, 17: 276–278.
  • Pearson, K. (1892). The Grammar of Science. Walter Scott.
  • –- (1907). "On the Influence of Past Experience on Future Expectation." Philosophical Magazine, 13: 365–378.
  • Pfanzagl, J. and Sheynin, O. (1996). "Studies in the History of Probability and Statistics: XLIV". A Forerunner of the $t$-distribution. Biometrika, 83: 891–898.
  • Porter, T. (1986). The Rise in Statistical Thinking: 1820–1900. Princeton University Press.
  • –- (2004). Karl Pearson: The Scientific Life in a Statistical Age. Princeton University Press.
  • Pratt, J. W. (1965). "Bayesian Interpretation of Standard Inference Statements." Journal of the Royal Statistical Society. Series B, 27.
  • –- (1995). "Foreword." In Eeckhoudt, L. and Gollier, C. (eds.), Risk: Evaluation, Management and Sharing. New York: Harvester Wheatsheaf.
  • Pratt, J. W., Raiffa, H., and Schlaifer, R. (1965). Introduction to Statistical Decision Theory–Preliminary Edition. McGraw-Hill.
  • Raiffa, H. and Schlaifer, R. (1961). Applied Statistical Decision Theory. Division of Research Graduate School of Business Administration, Harvard University.
  • Ramsey, F. P. (1926). "Truth and Probability." Published in 1931 as Foundations of Mathematics and Other Logical Essays, Ch. VII, pp. 156–198. Edited by R.B. Braithwaite. Kegan, Paul, Trench, Trubner & Co., London. Reprinted in Kyburg, H. E. and Smokler, H. E. eds. (1964). Studies in Subjective Probability. Wiley, New York, 61-92.
  • Robbins, H. (1951). "Asymptotically Subminimax Solutions of Compound Statistical Decision Problems." In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, volume 1, 131–148. Berkeley.
  • –- (1956). "An Empirical Bayes Approach to Statistics." In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, volume 1, 157–163. University of California Press.
  • –- (1964). "The Empirical Bayes Approach to Statistical Decision Problems." Annals of Mathematical Statistics, 35: 1–20.
  • Ross, I. and Tukey, J. W. (1975). Index to Statistics and Probability: Permuted Titles, A–-Microbiology. Los Altos, CA: R&D Press.
  • Rubin, H. (1949). "The Existence of Measurable Utility and Psychological Probability." Statistics 331, Cowles Commission Discussion Paper. 5 pp.
  • Savage, L. J. (1951). "The Theory of Statistical Decision." Journal of the American Statistical Association, 46: 55–67. Reprinted in Savage, Leonard J. (1981). The Writings of Leonard Jimmie Savage: A Memorial Selection. American Statistical Association and Institute of Mathematical Statistics, Washington, DC, 201-213.
  • –- (1952). "Review of Logical Foundations of Probability by Rudolph Carnap." Econometrica, 29: 688–1690.
  • –- (1954). The Foundations of Statistics. New York: Wiley, second revised paperback edition, dover, new york, 1972 edition.
  • –- (1960). "Unpublished Reading Note." Reproduced in Dale [Dale:1999?] as an Appendix, pp. 597-602.
  • –- (1961). "The Foundations of Statistical Inference Reconsidered." In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, volume 1, 575–586.
  • –- (1962). The Foundations of Statistical Inference. A Discussion. London: Methuen. G. Barnard and D.R. Cox, eds.
  • –- (1970). "Reading Suggestions for the Foundations of Statistics." American Statistician, 24: 23–27. [Reprinted in Savage, Leonard J. (1981). The Writings of Leonard Jimmie Savage: A Memorial Selection. American Statistical Association and Institute of Mathematical Statistics, Washington, DC, 536-546.].
  • –- (1976). "On Rereading R.A." Fisher (with discussion) (J.W. Pratt, ed.). Annals of Statistics, 4: 441–500.
  • –- (1981). The Writings of Leonard Jimmie Savage: A Memorial Selection. Washington, DC: American Statistical Association and Institute of Mathematical Statistics.
  • Schlaifer, R. (1959). Probability and Statistics for Business Decisions. New York: McGraw-Hill.
  • Scott, A. and Smith, T. (1969). "Estimation for Multi-Stage Surveys." Journal of the American Statistical Association, 64: 830–840.
  • Seidenfeld, T. (1992). "R.A. Fisher's Fiducial Argument and Bayes' Theorem." Statistical Science, 7: 358–368.
  • Seneta, E. (1998). "Early Influences on Probability and S "atistics in the Russian Empire. Archive for History of Exact Sciences, 53: 201–213.
  • Shafer, G. and Vovk, V. (2003). "The Sources of Kolmogorov's Grundbegriffe." Working Paper #4. Available at http://www.probabilityandfinance.com.
  • Sheynin, O. B. (1989). "A." A. Markov's Work on Probability." Archive for History of Exact Sciences, 39: 337–377. [Errata in 40 (1989), 387.].
  • –- (2004). "Fechner as a Statistician." British Journal of Mathematical and Statistical Psychology, 57: 53–72.
  • Smith, A. F. M. (1995). "A Conversation with Dennis Lindley." Statistical Science, 10: 305–319.
  • Stigler, S. M. (1978). "Francis Ysidro Edgeworth, Statistician." Journal of the Royal Statistical Society, Series A, 141: 287–322. (Also available with some corrections as Chapter 5 of Stigler, Stephen M. (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press, Cambridge, MA.).
  • –- (1980). "Stigler's Law of Eponymy." Transactions of the New York Academy of Sciences, Ser. 2, 39: 147–158. (Also available as Chapter 14 of Stigler, Stephen M. (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press, Cambridge, MA.).
  • –- (1982). "Thomas Bayes' Bayesian Inference." Journal of the Royal Statistical Society, Series A, 145: 250–258.
  • –- (1983). "Who Discovered Bayes' Theorem?" American Statistician, 37: 290–296. (Also available with some corrections as Chapter 15 of Stigler, Stephen M. (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press, Cambridge, MA.).
  • –- (1986). The History of Statistics: The Measurement of Uncertainty Before 1900. Cambridge, MA: Harvard University Press.
  • –- (1986). "Laplace's 1774 Memoir on Inverse Probability." Statistical Science, 1: 359–363.
  • –- (1999). Statistics on the Table: The History of Statistical Concepts and Methods. Cambridge, MA: Harvard University Press.
  • –- (2004). "How Ronald Fisher Became a Mathematical Statistician." Presented at Journée “Bernard Bru", Université de Paris VI, April 2, 2004.
  • Student (1908). "The Probable Error of a Mean." Biometrika, 6: 1–25.
  • Suppes, P. (1956). "The Role of Subjective Probability and Utility in Decision-making." In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, volume 5, 61–73.
  • Tiao, G. and Zellner, A. (1964). "Bayes' Theorem and the Use of Prior Knowledge in Regression Analysis." Biometrika, 51: 219–230.
  • Tukey, J. W. (1990). "The Collected Works of John W. Tukey, Volume VI: More Mathematical, 1938 - 1984." In Mallows, C. L. (ed.), The Collected Works of John W. Tukey, Volume VI: More Mathematical, 1938 - 1984, 119–148. Pacific Grove, CA: Wadsworth.
  • –- (1990). "The Present State of Fiducial Probability." In Mallows), C. L. (ed.), The Collected Works of John W. Tukey, Volume VI: More Mathematical, 1938 - 1984, volume VI, 55–118. Pacific Grove, CA: Wadsworth.
  • von Mises, R. (1928). Wahrscheinlichkeitsrechnung, Statistik und Wahrheit. Dover.
  • –- (1941). "On the Foundations of Probability and Statistics." Annals of Mathematical Statistics, 12: 191–205.
  • –- (1942). "On the Correct Use of Bayes' Formula." Annals of Mathematical Statistics, 13: 156–165.
  • von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton: Princeton University Press. (Paperback edition, 1980.).
  • Wald, A. (1939). "Contributions to the Theory of Statistical Estimation and Testing – A Hypotheses." Annals of Mathematical Statistic, 10: 299–326.
  • –- (1947). "An Essentially Complete Class of Admissible Decision Functions." Annals of Mathematical Statistics, 18: 549–555.
  • –- (1947). Sequential Analysis. New York: Wiley. (Paperback edition, Dover, New York, 1973.).
  • –- (1950). Statistical Decision Functions. New York: Wiley.
  • Wallis, W. A. (1980). "The Statistical Research Group, 1942–1945." Journal of the American Statistical Association, 75: 320–335.
  • –- (1981). "Memorial Tribute." In Savage, Leonard J. The Writings of Leonard Jimmie Savage: A Memorial Selection, 11–24. Washington, DC: American Statistical Association and Institute of Mathematical Statistics.
  • Wilks, S. S. (1936). "Discussion of Ernest Nagel: `The Meaning of Probability." Journal of the American Statistical Association, 31: 29–30.
  • Wrinch, D. and Jeffreys, H. (1919). "On Some Aspects of the Theory of Probability." Philosophical Magazine, 38: 715–731.
  • Zabell, S. (1982). "W.E. Johnson's `Sufficientness' Postulate." Annals of Statistics, 10: 1090–1099.
  • –- (1989). "R.A. Fisher on the History of Inverse Probability." Statistical Science, 4: 247–256.
  • –- (1989). "R.A. Fisher on the History of Inverse Probability: Rejoinder." Statistical Science, 4: 261–263.
  • Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. New York: Wiley.