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.
Similar content being viewed by others
References
Aitkin M. (2010) Statistical inference: A Bayesian/likelihood approach. CRC Press, New York
Basu D. (1988) Statistical information and likelihood: A collection of criticalessays by Dr. D. Basu. Springer–Verlag, New York
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
Berger J. (1985) Statistical decision theory and Bayesian analysis (2nd ed.). Springer-Verlag, New York
Berger J. (2003) Could Fisher, Jeffreys and Neyman have agreed on testing?. Statistical Science 18: 1–32
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
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
Berger J., Jefferys W. (1992) Sharpening Ockham’s razor on a Bayesian strop. American Statistics 80: 64–72
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
Carnap R. (1952) Logical foundations of probability. University of Chicago Press, Chicago
DeGroot M. (1970) Optimal statistical decisions. McGraw-Hill, New York
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
Hartigan J. A. (1983) Bayes theory. Springer-Verlag, New York
Hwang J., Casella G., Robert C., Wells M., Farrel R. (1992) Estimation of accuracy in testing. Annals of Statistics 20: 490–509
Jeffreys H. (1939) Theory of probability (1st ed.). The Clarendon Press, Oxford
Kass R., Raftery A. (1995) Bayes factors. Journal of the American Statistical Association 90: 773–795
Keynes J. M. (1921) A treatise on probability. Macmillan, London
MacKay D. J. C. (2002) Information theory, inference & learning algorithms. Cambridge University Press, Cambridge
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
Moreno E., Girón F., Casella G. (2010) Consistency of objective Bayes factors as the model dimension grows. Annals of Statistics 38: 1937–1952
O’Hagan A. (1995) Fractional Bayes factors for model comparisons. ournal of the Royal Statistical Society: Series B 57: 99–138
Pérez J., Berger J. (2002) Expected-posterior prior distributions for model selection. Biometrika 89: 491–512
Robert C. (2007) The Bayesian choice. Springer-Verlag, New York
Robert, C. (2010). An attempt at reading Keynes’ treatise on probability. International Statistical Review, 79, 1–15.
Robert, C., Chopin, N., & Rousseau, J. (2009). Theory of probability revisited (with discussion). Statistical Science, 24(2), 141–172; 191–194.
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
Schervish M. (1995) Theory of statistics. Springer-Verlag, New York
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
Templeton A. (2008) Statistical hypothesis testing in intraspecific phylogeography: nested clade phylogeographical analysis vs. approximate Bayesian computation. Molecular Ecology 18(2): 319–331
Templeton A. (2010) Coherent and incoherent inference in phylogeography and human evolution. Proceedings of the National Academy of Sciences 107(14): 6376–6381
von Mises R. (1957) Probability, statistics, and truth. Dover, New York
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11238-012-9298-3