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Bayesian and Non-Bayesian Approaches to Statistical Inference: A Personal View

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Statistical Methods and Applications from a Historical Perspective

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Abstract

Bayesian and non-bayesian approaches to statistical inference are compared giving particular attention to the emerging field of causal statistical inference and causal statistical decision theory. After a brief review of the evolution of statistical inference, as extraction of information and identification of models from data, the problematic issues of causal inference and causal decision theory will be reviewed. The aim is to provide some basic ideas for unifying the different approaches and for strengthening the future of statistics as a discipline.

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Notes

  1. 1.

    On the contributions of Gini to the foundations of probability and statistical inference I strongly recommend a forthcoming paper by Piccinato (2011).

References

  • Allais, M.: Le comportament de l’homme rationel devant le risque: critique des axiom et postulates de l’ecole americane. Econometrica 21, 503–546 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  • Armendt, B.: A foundations of causal decision theory. Topoi 5, 3–19 (1986)

    Article  MathSciNet  Google Scholar 

  • Bayes, T.: Essay towards solving a problem in the doctrine of chances. Philos. Trans. R. Soc. Lond. 53, 370–418 (1763)

    Google Scholar 

  • Bell, D.E., Raiffa, H., Tversky, A.: Decision Making. Cambridge University Press, Cambridge (1988)

    Book  MATH  Google Scholar 

  • Carnap, R.: Logical Foundations of Probability. Chicago University Press, Chicago (1950)

    MATH  Google Scholar 

  • Chiandotto, B., Bacci, S.: Decisioni razionali per il governo dell’università, un prerequisito essenziale: la teoria dell’utilità. Università degli Studi di Firenze (2004)

    Google Scholar 

  • Cox, D.R.: Some problems connected with statistical inference. Ann. Math. Stat. 29, 357–372 (1958)

    Article  MATH  Google Scholar 

  • Cox, D.R., Wermuth, N.: Causality: a statistical view. Int. Stat. Rev. 72, 285–305 (2004)

    Article  Google Scholar 

  • Dawid, A.P.: Causal inference without counterfactuals. J. Am. Stat. Assoc. 95, 407–448 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Dawid, A.P.: Influence diagrams for causal modelling and inference. Int. Stat. Rev. 70, 161–189 (2002)

    Article  MATH  Google Scholar 

  • De Finetti, B.: La prévision: ses lois logiques, ses source subjectives. Ann. del’Institut Henri Poincarré 24, 17–24 (1937)

    Google Scholar 

  • Fishburn, P.: A mixture-set axiomatization of conditional subjective expected utility. Econometrica 41, 1–25 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • Fisher, R.A.: Inverse probability. Math Proc. Camb. Philos. Soc. 26, 528–535 (1930)

    Article  MATH  Google Scholar 

  • Fisher, R.A.: The logic of Inductive inference (with discussion). J. R. Stat. Soc. 98, 39–82 (1935)

    Article  Google Scholar 

  • Fisher, R.A.: Statistical Method and Scientific Inference. Oliver and Boyd, Edinburgh (1956)

    Google Scholar 

  • Freedman, D.: From association to causation: some remarks on the history of statistics. Stat. Sci. 14, 243–258 (1999)

    Article  MATH  Google Scholar 

  • Frosini, B.V.: Causality and causal models: a conceptual perspective. Int. Stat. Rev. 74, 305–334 (2006)

    Article  Google Scholar 

  • Gibbard, A., Harper, W.: Counterfactuals and two kinds of expected utility. In: Harper, W., Stalnaker, R., Pearce, G. (eds.) Conditionals, Belief, Decision, Chance, and Time, pp. 153–190. Dordrecht-Reidel, Dordrecht (1976)

    Google Scholar 

  • Gini, C.: I test di significatività, Atti della VII Riunione della Società Italiana di Statistica, Roma (1943)

    Google Scholar 

  • Good, I.J.: Weights of evidence, corroboration, explanatory power, information and utility of experiment. J. R. Stat. Soc. Ser. B Stat. Methodol. 22, 319–331 (1960)

    MATH  MathSciNet  Google Scholar 

  • Heckerman, D., Shachter, R.: Decision-theoretic foundations for causal reasoning. J. Artif. Intell. Res. 3, 405–430 (1995)

    MATH  Google Scholar 

  • Heckerman, D., Shachter, R.: Discussion in Pearl, J.: Statistics and causal inference: a review. Test 12, 101–165 (2003)

    Article  MathSciNet  Google Scholar 

  • Holland, P.: Statistics and causal inference. J. Am. Stat. Assoc. 81, 945–960 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Holland, P., Rubin, D.: Causal inference in retrospective studies. Eval. Rev. 13, 203–231 (1988)

    Article  Google Scholar 

  • Howard, R.A., Matheson, J.E.: Influence diagrams. In: Howard, R.A., Matheson, J.E. (eds.) Readings in the Principles and Applications of Decision Analysis. Strategic Decision Group, Menlo Park (1984)

    Google Scholar 

  • Hume, D.: A Treatise of Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects. Book 1: Of the Understanding (2003). The Project Gutenberg EBook. Release Date: December, 2003

    Google Scholar 

  • Jeffreys, H.: Scientific Inference. Cambridge University Press, Cambridge (1931)

    Google Scholar 

  • Joyce, J.: The Foundations of Causal Decision Theory. Cambridge University Press, Cambridge (1999)

    Book  MATH  Google Scholar 

  • Joyce, J.: A defense of imprecise credence and decision making. Philos. Perspect. 24, 281–323 (2010)

    Article  Google Scholar 

  • Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–293 (1979)

    Article  MATH  Google Scholar 

  • Keynes, J.M.: A Treatise on Robability. MacMillan & Co. London (1921)

    Google Scholar 

  • Laplace, P.S.: Théorie analitique the probabilities, 3rd edn. (1820). Courcier, Paris (1812)

    Google Scholar 

  • Lauritzen, S.L.: Discussion on causality in Rubin, D.B. (2004): Direct and indirect causal effects via potential outcomes. Scand. J. Stat. 31, 161–170 (2004)

    Google Scholar 

  • Lauritzen, S., Richardson, T.: Chain graph models and their causal interpretations (with discussion). J. R. Stat. Soc. Ser. B Stat. Methodol. 64, 321–361 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  • Lewis, D.: Causal decision theory. Australas. J. Philos. 59, 5–30 (1981)

    Article  Google Scholar 

  • Lindley, D.V.: Understanding Uncertainty. Wiley, Hoboken (2006)

    Book  MATH  Google Scholar 

  • Machina, M.J.: Expected utility analysis without the independence axiom. Econometrica 50, 227–323 (1982)

    Google Scholar 

  • Mealli, F., Pacini, B., Rubin, D.B.: Statistical inference for causal effects. In: Kenett, R., Salini, S. (eds.) Modern Analysis of Customer Satisfaction Surveys. Wiley, Chichester (2011)

    Google Scholar 

  • Neyman, J., Pearson, E.S.: On the use and interpretation of certain test criteria for purposes of statistical inference. Part. I and II. Biometrika 20A, 175–240 and 263–294 (1928)

    Google Scholar 

  • Pearl, J.: Causal diagrams for empirical research. Biometrika 82(4), 669–710 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  • Pearl, J.: Causality: Models, Reasoning, and Inference, 2nd edn. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  • Pearl, J.: The causal foundations of structural equation modeling. In: Hoyle, R.H. (ed) Handbook of Structural Equation Modeling. Guilford Press, New York (2011)

    Google Scholar 

  • Piccinato, L.: Gini’s criticism to the theory of inference: a missed opportunity. Metron 69, 101–117 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  • Pompilj, G.: Logica della conformità. Archimede 4, 22–28 (1952)

    MATH  Google Scholar 

  • Pompilj, G.: Teoria dei campioni, Applicazioni alla sperimentazione, alla produttività e alle rilevazioni campionarie. Partial reprint (1956), Veschi, Roma (1961)

    Google Scholar 

  • Popper, K.R.: The Logic of Scientific Discovery. First version of this book appeared as Logic der Forschung, 1934. Hutchison Education, London (1959)

    Google Scholar 

  • Quiggin, J.: Generalized Expected Utility the Rank-Dependent Model. Kluwer, Boston (1993)

    Book  Google Scholar 

  • Ramsey, F.P.: Truth and probability. In: Braithwaite, R.B. (ed.) The Foundations of Mathematics and Other Logical Essays, pp. 56–198. Routledge & Kegan Paul, London (1931)

    Google Scholar 

  • Roy, B.: Decision science or decision-aid science? Eur. J. Oper. Res. 66, 184–203 (1993)

    Article  Google Scholar 

  • Rubin, D.B.: Estimating causal effects of treatment s in randomized and non-randomized studies. J. Educ. Psychol. 66, 688–701 (1974)

    Article  Google Scholar 

  • Rubin, D.B.: Direct and indirect causal effects via potential outcomes. Scand. J. Stat. 31, 161–170 (2004)

    Article  MATH  Google Scholar 

  • Savage, L.J.: The theory of statistical decision. J. Am. Stat. Assoc. 46, 55–67 (1951)

    Article  MATH  Google Scholar 

  • Savage, L.J.: The Foundations of Statistics. Wiley, New York (1954)

    MATH  Google Scholar 

  • Skyrms, B.: Causal Necessity. Yale University Press, New Haven (1979)

    Google Scholar 

  • Smith, C.A.B.: Consistency in statistical inference and decision. J. R. Stat. Soc. Ser. B Stat. Methodol. 25, 1–37 (1961)

    Google Scholar 

  • Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction and Search, Springer, 2nd edn. MIT Press, Cambridge (2000)

    Google Scholar 

  • Tsoukiàs, A.: On the concept of decision aiding process: an operational perspective. Ann. Oper. Res. 154, 3–27 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk. Uncertain. 5, 297–323 (1992)

    Article  MATH  Google Scholar 

  • Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, 2nd edn. Princeton University Press, Princeton (1947)

    MATH  Google Scholar 

  • Woodword, J.: Making things happen: a theory of causal explanation. In: Oxford Studies in the Philosophy of Science. Oxford University Press, New York (2003)

    Google Scholar 

  • White, H., Chalak, K.: A Unified Framework for Defining and Identifying causal Effects, UCSD Department of Economics Working Paper, pp. 1–53 (2006)

    Google Scholar 

  • Wright, S.: Correlation and causation. J. Agric. Res. 20, 557–585 (1921)

    Google Scholar 

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Correspondence to Bruno Chiandotto .

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Chiandotto, B. (2014). Bayesian and Non-Bayesian Approaches to Statistical Inference: A Personal View. In: Crescenzi, F., Mignani, S. (eds) Statistical Methods and Applications from a Historical Perspective. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-05552-7_1

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