Statistical Science

Probability, Causality and the Empirical World: A Bayes–de Finetti–Popper– Borel Synthesis

A. P. Dawid

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This article expounds a philosophical approach to Probability and Causality: a synthesis of the personalist Bayesian views of de Finetti and Popper’s falsificationist programme. A falsification method for probabilistic or causal theories, based on “Borel criteria,” is described. It is argued that this minimalist approach, free of any distracting metaphysical inputs, provides the essential support required for the conduct and advance of Science.

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Statist. Sci., Volume 19, Number 1 (2004), 44-57.

First available in Project Euclid: 14 July 2004

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Borel criterion calibration falsification Jeffreys’s law


Dawid, A. P. Probability, Causality and the Empirical World: A Bayes–de Finetti–Popper– Borel Synthesis. Statist. Sci. 19 (2004), no. 1, 44--57. doi:10.1214/088342304000000125.

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  • Aldous, D. J. (1981). Representations for partially exchangeable arrays of random variables. J. Multivariate Anal. 11 581--598.
  • Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions 53 370--418 [Reprinted as Bayes (1958).]
  • Bayes, T. (1958). An essay towards solving a problem in the doctrine of chances. Biometrika 45 293--315. [Reprint of Bayes (1763), with a biographical note by G. A. Barnard.]
  • Bernoulli, J. (1713). Ars Conjectandi. Thurnisius, Basel.
  • Blackwell, D. and Dubins, L. E. (1962). Merging of opinions with increasing information. Ann. Math. Statist. 33 882--886.
  • Borel, E. (1943). Les Probabilités et la vie. Presses Universitaires de France. [English translation published (1962) as Probabilities and Life. Dover, New York.]
  • Consonni, G. and Dawid, A. P. (1985). Invariant normal Bayesian linear models and experimental designs. In Bayesian Statistics 2 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 629--643. North-Holland, Amsterdam.
  • Cournot, A. A. (1843). Exposition de la théorie des chances et des probabilités. Hachette, Paris.
  • Dawid, A. P. (1977). Invariant distributions and analysis of variance models. Biometrika 64 291--297.
  • Dawid, A. P. (1979). Conditional independence in statistical theory (with discussion). J. Roy. Statist. Soc. Ser. B 41 1--31.
  • Dawid, A. P. (1982a). Intersubjective statistical models. In Exchangeability in Probability and Statistics (G. Koch and F. Spizzichino, eds.) 217--232. North-Holland, Amsterdam.
  • Dawid, A. P. (1982b). The well-calibrated Bayesian (with discussion). J. Amer. Statist. Assoc. 77 605--613. [Reprinted in Hamouda and Rowley (1997) 165--173.]
  • Dawid, A. P. (1984a). Causal inference from messy data. Discussion of ``On the nature and discovery of structure,'' by J. W. Pratt and R. Schlaifer. J. Amer. Statist. Assoc. 79 22--24. [Reprinted in Poirier (1994) 1 368--370.]
  • Dawid, A. P. (1984b). Discussion of ``Extreme point models in statistics,'' by S. L. Lauritzen. Scand. J. Statist. 11 85.
  • Dawid, A. P. (1984c). Present position and potential developments: Some personal views. Statistical theory. The prequential approach (with discussion). J. Roy. Statist. Soc. Ser. A 147 278--292.
  • Dawid, A. P. (1985a). Calibration-based empirical probability (with discussion). Ann. Statist. 13 1251--1285. [Reprinted in Hamouda and Rowley (1997) 174--208.]
  • Dawid, A. P. (1985b). The impossibility of inductive inference. Discussion of ``Self-calibrating priors do not exist,'' by D. Oakes. J. Amer. Statist. Assoc. 80 340--341.
  • Dawid, A. P. (1985c). Probability, symmetry and frequency. British J. Philos. Sci. 36 107--128.
  • Dawid, A. P. (1986a). A Bayesian view of statistical modelling. In Bayesian Inference and Decision Techniques (P. K. Goel and A. Zellner, eds.) 391--404. North-Holland, Amsterdam.
  • Dawid, A. P. (1986b). Probability forecasting. In Encyclopedia of Statistical Sciences 7 210--218. Wiley, New York.
  • Dawid, A. P. (1988). Symmetry models and hypotheses for structured data layouts. J. Roy. Statist. Soc. Ser. B 50 1--34.
  • Dawid, A. P. (1997). Prequential analysis. In Encyclopedia of Statistical Sciences, Update Volume 1 464--470. Wiley, New York.
  • Dawid, A. P. (2000). Causal inference without counterfactuals (with discussion). J. Amer. Statist. Assoc. 95 407--448.
  • Dawid, A. P. (2002). Influence diagrams for causal modelling and inference. Internat. Statist. Rev. 70 161--189. [Corrigenda (2002) 70 437.]
  • Dawid, A. P. (2003). Causal inference using influence diagrams: The problem of partial compliance (with discussion). In Highly Structured Stochastic Systems (P. J. Green, N. L. Hjort and S. Richardson, eds.) 45--81. Oxford Univ. Press.
  • Dawid, A. P. and Vovk, V. (1999). Prequential probability: Principles and properties. Bernoulli 5 125--162.
  • de Finetti, B. (1937). Foresight: Its logical laws, its subjective sources. Ann. Inst. H. Poincaré 7 1--68. [Translated by H. E. Kyburg in Kyburg and Smokler (1964) 93--158.]
  • de Finetti, B. (1974--1975). Theory of Probability 1, 2. Wiley, New York. [Italian original published (1970) by Einaudi, Torino.]
  • Diaconis, P. and Freedman, D. (1980). de Finetti's theorem for Markov chains. Ann. Probab. 8 115--130.
  • Goodman, N. (1954). Fact, Fiction, and Forecast. Athlone, London.
  • Hamouda, O. F. and Rowley, J. C. R., eds. (1997). Probability Concepts, Dialogue and Beliefs. Elgar, Cheltenham, UK.
  • Howson, C. and Urbach, P. (1993). Scientific Reasoning: The Bayesian Approach, 2nd ed. Open Court, La Salle, IL.
  • Kalai, E. and Lehrer, E. (1993). Rational learning leads to Nash equilibrium. Econometrica 61 1019--1045.
  • Kyburg, H. E. and Smokler, H. E., eds. (1964). Studies in Subjective Probability. Wiley, New York.
  • Lauritzen, S. L. (1988). Extremal Families and Systems of Sufficient Statistics. Lecture Notes in Statist. 49. Springer, New York.
  • Lauritzen, S. L. (2003). Rasch models with exchangeable rows and columns (with discussion). In Bayesian Statistics 7 (J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.) 215--232. Oxford Univ. Press.
  • Lindley, D. V. (1965). An Introduction to Probability and Statistics from a Bayesian Viewpoint. Cambridge Univ. Press. (1 Part I: Probability, 2 Part II: Inference.)
  • Miller, R. I. and Sanchirico, C. W. (1999). The role of absolute continuity in ``merging of opinions'' and ``rational learning.'' Games Econom. Behav. 29 170--190.
  • Muth, J. F. (1961). Rational expectations and the theory of price movements. Econometrica 29 315--335.
  • Pearl, J. (2000). Causality. Cambridge Univ. Press.
  • Poirier, D. J., ed. (1994). The Methodology of Econometrics 1, 2. Elgar, Cheltenham, UK.
  • Popper, K. R. (1959). The Logic of Scientific Discovery. Hutchinson, London. (German original published in 1934.)
  • Popper, K. R. (1982). The Open Universe. Hutchinson, London.
  • Popper, K. R. (1983). Realism and the Aim of Science. Hutchinson, London.
  • Ramsey, F. P. (1926). Truth and probability. In The Foundations of Mathematics and Other Logical Essays (R. B. Braithwaite, ed.) 58--100. Routledge and Kegan Paul, London. [Reprinted in Kyburg and Smokler (1964) 61--92.]
  • Robins, J. M. (1989). The analysis of randomized and nonrandomized AIDS treatment trials using a new approach to causal inference in longitudinal studies. In Health Service Research Methodology: A Focus on AIDS (L. Sechrest, H. Freeman and A. Mulley, eds.) 113--159. NCSHR, U.S. Public Health Service.
  • Rubin, D. B. (1978). Bayesian inference for causal effects: The role of randomization. Ann. Statist. 6 34--58.
  • Savage, L. J. (1954). The Foundations of Statistics. Wiley, New York.
  • Schervish, M. J. (1985). Discussion of ``Calibration-based empirical probability,'' by A. P. Dawid. Ann. Statist. 13 1274--1282.
  • Seillier-Moiseiwitsch, F. and Dawid, A. P. (1993). On testing the validity of sequential probability forecasts. J. Amer. Statist. Assoc. 88 355--359.
  • Shafer, G. (1996). The Art of Causal Conjecture. MIT Press.
  • Shafer, G. and Vovk, V. G. (2001). Probability and Finance: It's Only a Game. Wiley, New York.
  • Ville, J. (1939). Étude critique de la notion de collectif. Gauthier-Villars, Paris.
  • von Mises, R. (1939). Probability, Statistics and Truth. Hodge, London. [German original published (1928) by J. Springer.]