Skip to main content
Log in

Error and inference: an outsider stand on a frequentist philosophy

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

This paper is an extended review of the book Error and Inference, edited by Deborah Mayo and Aris Spanos, about their frequentist and philosophical perspective on testing of hypothesis and on the criticisms of alternatives like the Bayesian approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Eric-Jan Wagenmakers, Quentin F. Gronau, … Alexander Etz

References

  • Aitkin M. (2010) Statistical inference: A Bayesian/likelihood approach. CRC Press, New York

    Book  Google Scholar 

  • Basu D. (1988) Statistical information and likelihood: A collection of criticalessays by Dr. D. Basu. Springer–Verlag, New York

    Google Scholar 

  • Beaumont M., Nielsen R., Robert C., Hey J., Gaggiotti O., Knowles L., Estoup A., Mahesh P., Coranders J., Hickerson M., Sisson S., Fagundes N., Chikhi L., Beerli P., Vitalis R., Cornuet J.-M., Huelsenbeck J., Foll M., Yang Z., Rousset F., Balding D., Excoffier L. (2010) In defense of model-based inference in phylogeography. Molecular Ecology 19(3): 436–446

    Article  Google Scholar 

  • Berger J. (1985) Statistical decision theory and Bayesian analysis (2nd ed.). Springer-Verlag, New York

    Google Scholar 

  • Berger J. (2003) Could Fisher, Jeffreys and Neyman have agreed on testing?. Statistical Science 18: 1–32

    Article  Google Scholar 

  • Berger J., Bernardo J. (1992) On the development of the reference prior method. In: Berger J., Bernardo J., Dawid A., Smith A. (eds) Bayesian statistics 4. Oxford University Press, London, pp 35–49

    Google Scholar 

  • Berger J., Ghosh J., Mukhopadhyay N. (2003) Approximations and consistency of Bayes factors as model dimension grows. Journal of Statistical Planning and Inference 112: 241–258

    Article  Google Scholar 

  • Berger J., Jefferys W. (1992) Sharpening Ockham’s razor on a Bayesian strop. American Statistics 80: 64–72

    Google Scholar 

  • Berger, J., & Wolpert, R. (1988). The likelihood principle (2nd ed.). IMS lecture notes—monograph series (Vol. 9). Hayward: IMS.

  • Birnbaum A. (1962) On the foundations of statistical inference. Journal of the American Statistical Association 57: 269–306

    Article  Google Scholar 

  • Carnap R. (1952) Logical foundations of probability. University of Chicago Press, Chicago

    Google Scholar 

  • DeGroot M. (1970) Optimal statistical decisions. McGraw-Hill, New York

    Google Scholar 

  • Gelman, A., & Shalizi, C. R. (2012). Philosophy and the practice of Bayesian statistics. British Journal of Mathematical and Statistical Psychology. doi:10.1111/j.2044-8317.2011.02037.x

  • Gigerenzer G. (2002) Calculated risks: How to know when numbers deceive you. Simon and Schuster, New York

    Google Scholar 

  • Hartigan J. A. (1983) Bayes theory. Springer-Verlag, New York

    Book  Google Scholar 

  • Hwang J., Casella G., Robert C., Wells M., Farrel R. (1992) Estimation of accuracy in testing. Annals of Statistics 20: 490–509

    Article  Google Scholar 

  • Jeffreys H. (1939) Theory of probability (1st ed.). The Clarendon Press, Oxford

    Google Scholar 

  • Kass R., Raftery A. (1995) Bayes factors. Journal of the American Statistical Association 90: 773–795

    Article  Google Scholar 

  • Keynes J. M. (1921) A treatise on probability. Macmillan, London

    Google Scholar 

  • MacKay D. J. C. (2002) Information theory, inference & learning algorithms. Cambridge University Press, Cambridge

    Google Scholar 

  • Mayo, D., & Cox, D. (2006). Frequentist statistics as a theory of inductive inference. In J. Rojo (Ed.), Optimality: The second Erich L. Lehmann symposium (pp. 77–97). Lecture note—monograph series. Beachwood, OH: Institute of Mathematical Statistics.

  • Mayo D. G. (1996) Error and the growth of experimental knowledge. University of Chicago Press, Chicago

    Google Scholar 

  • Moreno E., Girón F., Casella G. (2010) Consistency of objective Bayes factors as the model dimension grows. Annals of Statistics 38: 1937–1952

    Article  Google Scholar 

  • O’Hagan A. (1995) Fractional Bayes factors for model comparisons. ournal of the Royal Statistical Society: Series B 57: 99–138

    Google Scholar 

  • Pérez J., Berger J. (2002) Expected-posterior prior distributions for model selection. Biometrika 89: 491–512

    Article  Google Scholar 

  • Robert C. (2007) The Bayesian choice. Springer-Verlag, New York

    Google Scholar 

  • Robert, C. (2010). An attempt at reading Keynes’ treatise on probability. International Statistical Review, 79, 1–15.

    Google Scholar 

  • Robert, C., Chopin, N., & Rousseau, J. (2009). Theory of probability revisited (with discussion). Statistical Science, 24(2), 141–172; 191–194.

    Google Scholar 

  • Robert C., Cornuet J.-M., Marin J.-M., Pillai N. (2011) Lack of confidence in ABC model choice. Proceedings of the National Academy of Sciences 108(37): 15112–15117

    Article  Google Scholar 

  • Schervish M. (1995) Theory of statistics. Springer-Verlag, New York

    Book  Google Scholar 

  • Spiegelhalter D. J., Best N. G., Carlin B. P., van der Linde A. (2002) Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society: Series B 64: 583–639

    Article  Google Scholar 

  • Templeton A. (2008) Statistical hypothesis testing in intraspecific phylogeography: nested clade phylogeographical analysis vs. approximate Bayesian computation. Molecular Ecology 18(2): 319–331

    Article  Google Scholar 

  • Templeton A. (2010) Coherent and incoherent inference in phylogeography and human evolution. Proceedings of the National Academy of Sciences 107(14): 6376–6381

    Article  Google Scholar 

  • von Mises R. (1957) Probability, statistics, and truth. Dover, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christian P. Robert.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Robert, C.P. Error and inference: an outsider stand on a frequentist philosophy. Theory Decis 74, 447–461 (2013). https://doi.org/10.1007/s11238-012-9298-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-012-9298-3

Keywords

Navigation