Abstract
From the outside, Bayesian statistics may seem like a closed little corner of probability. Once a prior is specified you compute! From the inside the field is filled with problems, conceptual and otherwise. This paper surveys some of what remains to be done and gives examples of the work in progress via a Bayesian peek into Feller volume I.
This work had its origin in conversations with Marco Scarsini. Distance has prevented us from working things out jointly. This paper was presented at the workshop, we thank Eugenio Regazzini, Dominico Costantini and Maria Carla Galavotti for their help. Art Dempster, Carl Morris, John Pratt, Abner Shimony and Sandy Zabell raised interesting questions incorporated herein.
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References
Aldous, D.: 1989, Probability Approximations via the Poisson dumping Heuristic, Springer Verlag, New York.
Bayer, D. and P. Diaconis: 1992, ‘Trailing the Dovetail Shuffle to its Lair’, Ann. Appl Prob. 2, 294–313.
Besag, J., P. J. Green, D. M. Higdon, and K. L. Mengersen: 1995, ‘Bayesian Computation and Stochastic Systems’ (with discussion), Stat. Sc. 10, 3–66.
Das Gupta, A.: 1995, Winning at Craps with a Random Die, Technical Report, Dept. of Statistics, Purdue University.
Dempster, A.: 1995, The Logic of Statistics, Tech. Report S-170, Harvard Statistics Dept.
Diaconis, P.: 1988, Group Representations in Probability and Statistics, IMS Lecture Notes, IMS, Hayward California.
Diaconis, P. and S. Holmes: 1996, A Bayesian Peek into Feller, Volume I, Preprint, Dept. of Mathematics, Harvard University.
Diaconis, P. and F. Mosteller: 1989, ‘Methods for Studying Coincidences’, J. Amer. Stat. Assoc. 84, 853–861.
Diaconis, P., M. McGrath, and J. Pitman: 1994, ‘Riffle Shuffles, Cycles and Descents’, Combinatorica 66, 379–386.
Diaconis, P. and L. Saloff-Coste: 1995, ‘What do we Know About the Metropolis Algorithm?’, Tech. Rep., Department of Mathematics, Harvard University.
Diaconis, P. and S. Zabell: 1982, ‘Updating Subjective Probability’, J. Amer. Stat. Assoc. 77, 822–830.
de Finetti, B.: 1937, ‘La prévision: ses lois logiques, ses sources subjectives’, Ann. Inst. Henri Poincaré 7, 1–68. English translation in H. Kyburg and H. Smokier (eds.), Studies in Subjective Probability, Wiley, New York (1964).
de Finetti, B.: 1974, 1975, Theory of Probability, Vols. 1 and 2, Wiley, New York.
Feller, W: 1968, An Introduction to Probability Theory and Its Applications, Volume 1, 3rd edition, Wiley, New York.
Fortini, S., R. Ladelli, and E. Regazzini: 1994, A Central Limit Theorem for Partially Exchangeable Random Variables, Technical Report. Istituto Per le Applicazioni della Matematica e dell’ Informatica, Via Ampère 56, Milano, Italy.
Freedman, D.: 1991, ‘Statistical Models and Shoe Leather’, in P. Marsden (ed.), Sociological Methodology, B. Blackwell, Washington, pp. 291–358.
Freedman, D.: 1995, ‘Some Issues in the Foundations of Statistics’, Foundations of Science 1(1), 19–39.
Freedman, D.: 1994, ‘From Association to Causation’, Technical Report, Berkely Statistics Department, to appear in Advances in Appl. Math.
Good, I. J.: 1965, The Estimation of Probabilities: An Essay on Bayesian, MIT Press, Cambridge, USA.
Good, I. J.: 1976, ‘On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency Tables’, Ann. Stat. 5, 1159–1189.
Hammersley, J. M. and D. C. Handscomb: 1964, Monte Carlo Methods, Wiley, New York.
Jeffrey, R.: 1983, The Logic of Decision, 2nd. ed., University Chicago Press.
Laplace, P.: 1812, Theorie Analytique des Probabilités, Courcier, Paris, 3rd ed. 1820 with supplements.
Montmort and Pierre Remond de: 1713, Essay d’analyse sur les jeux de hasard, 2nd. ed., Jaques Quillau, Paris.
Scarsini, M.: 1992, A Bayesian Analysis of Gambler’s Ruin, Unpublished Manuscript.
Stein, C.: 1986, Approximate Computation of Expectations, IMS Lecture Notes and Mono-graphs, Hayward, California.
Stein, C.: 1990, ‘Applications of Newton’s Identities to a General Birthday Problem and to the Poisson Binomial Distribution’, Tech. Report, Statistics Dept., Stanford.
Takács, L.: 1980, The Problem of Coincidences’, Arch. Hist. Exact. Sci. 21, 229–244.
Tukey, J. W.: 1977, Exploratory Data Analysis, Addison Wesley, Reading, Mass.
West, M. and Harrison, J.: 1989, Bayesian Forecasting and Dynamic Models, Springer Verlag, New York.
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Diaconis, P., Holmes, S. (1997). Are there Still Things to Do in Bayesian Statistics?. In: Costantini, D., Galavotti, M.C. (eds) Probability, Dynamics and Causality. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5712-4_1
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