Philosophy of statistics

Statistics are way important.

Contents

  1. Issues and positions
    1. Problem of induction
    2. Probability and uncertainty
    3. Early investigators
    4. Foundations of statistics
    5. Statistical hypothesis testing
    6. Point estimation and confidence intervals
    7. Systematic uncertainties
    8. P-value controversy
    9. Machine learning
    10. Implications for the realism debate
  2. My thoughts
  3. Annotated bibliography
    1. Mayo, D.G. (1996). Error and the Growth of Experimental Knowledge.
    2. Cowan, G. (1998). Statistical Data Analysis.
    3. James, F. (2006). Statistical Methods in Experimental Physics, 2nd Ed.
    4. Cowan, G. et al. (2011). Asymptotic formulae for likelihood-based tests of new physics.
    5. ATLAS Collaboration. (2012). Combined search for the Standard Model Higgs boson in (pp) collisions at () = 7 TeV with the ATLAS detector.
    6. Cranmer, K (2015). Practical statistics for the LHC.
    7. More articles to do
  4. Links and encyclopedia articles
    1. SEP
    2. IEP
    3. Scholarpedia
    4. Wikipedia
    5. Others
  5. References

Issues and positions

Problem of induction

Probability and uncertainty

Early investigators

Foundations of statistics

Statistical hypothesis testing

Point estimation and confidence intervals

Systematic uncertainties

Figure 1: Classification of measurement uncertainties (philosophy-in-figures.tumblr.com).

Figure 1: Classification of measurement uncertainties (philosophy-in-figures.tumblr.com).

P-value controversy

Machine learning

Implications for the realism debate

My thoughts

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Annotated bibliography

Mayo, D.G. (1996). Error and the Growth of Experimental Knowledge.

My thoughts


Cowan, G. (1998). Statistical Data Analysis.

My thoughts


James, F. (2006). Statistical Methods in Experimental Physics, 2nd Ed.

My thoughts


Cowan, G. et al. (2011). Asymptotic formulae for likelihood-based tests of new physics.

My thoughts


ATLAS Collaboration. (2012). Combined search for the Standard Model Higgs boson in \(pp\) collisions at \(\sqrt{s}\) = 7 TeV with the ATLAS detector.

My thoughts


Cranmer, K (2015). Practical statistics for the LHC.

My thoughts


SEP

IEP

Scholarpedia

Wikipedia

Others

References

Aldrich, J. (1997). R. A. Fisher and the making of maximum likelihood 1912-1922. Statistical Science, 12, 162–176.

ATLAS Collaboration. (2012). Combined search for the Standard Model Higgs boson in \(pp\) collisions at \(\sqrt{s}\) = 7 TeV with the ATLAS detector. Physical Review D, 86, 032003. https://arxiv.org/abs/1207.0319

Benjamin, D.J. et al. (2017). Redefine statistical significance. PsyArXiv. July 22, 2017. https://psyarxiv.com/mky9j/

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

Cowan, G. (1998). Statistical Data Analysis. Clarendon Press.

———. (2012). Discovery sensitivity for a counting experiment with background uncertainty. https://www.pp.rhul.ac.uk/~cowan/stat/notes/medsigNote.pdf

———. (2016). Statistics. In C. Patrignani et al. (Particle Data Group), Chinese Physics C, 40, 100001. http://pdg.lbl.gov/2016/reviews/rpp2016-rev-statistics.pdf.

Cowan, G., Cranmer, K., Gross, E., & Vitells, O. (2011). Asymptotic formulae for likelihood-based tests of new physics. European Physical Journal C, 71, 1544. https://arxiv.org/abs/1007.1727

Cramér, H. (1946). A contribution to the theory of statistical estimation. Skandinavisk Aktuarietidskrift, 29, 85–94.

Cranmer, K. (2015). Practical statistics for the LHC. https://arxiv.org/abs/1503.07622

Feldman, G. J., & Cousins, R. D. (1998). A unified approach to the classical statistical analysis of small signals. Physical Review D, 57, 3873. https://arxiv.org/abs/physics/9711021

Fisher, R. A. (1912). On an absolute criterion for fitting frequency curves. Statistical Science, 12, 39–41.

———. (1915). Frequency distribution of the values of the correlation coefficient in samples of indefinitely large population. Biometrika, 10, 507–521.

Fréchet, M. (1943). Sur l’extension de certaines évaluations statistiques au cas de petits échantillons. Revue de L’Institut International de Statistique, 11, 182–205.

Good, I. J. (1988). The interface between statistics and philosophy of science. Statistical Science, 3, 386–397.

Hacking, I. (2001). An Introduction to Probability and Inductive Logic. Cambridge University Press.

Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.). Springer.

Huber, F. (2007). Confirmation and induction. Internet Encyclopedia of Philosophy. http://www.iep.utm.edu/conf-ind/

Hume, D. (2007). An Enquiry Concerning Human Understanding. (P. Millican, Ed.). Oxford University Press. (Originally published in 1748).

James, F. (2006). Statistical Methods in Experimental Particle Physics. World Scientific.

Kendall, M. G. (1946). The Advanced Theory of Statistics, Vol.II. London: Charles Griffin & Company.

Leemis, L. M., & McQueston, J. T. (2008). Univariate distribution relationships. The American Statistician, 62, 45–53.

Mayo, D. G. (1981). In defense of the Neyman-Pearson theory of confidence intervals. Philosophy of Science, 48, 269–280.

———. (1996). Error and the Growth of Experimental Knowledge. Chicago University Press.

Neyman, J., & Pearson, E. S. (1933). On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society A, 231, 289–337.

Rao, C. R. (1945). Information and the accuracy attainable in the estimation of statistical parameters. Bulletin of the Calcutta Mathematical Society, 37, 81–91.

———. (1947). Minimum variance and the estimation of several parameters. In Mathematical Proceedings of the Cambridge Philosophical Society. 43, 280–283. Cambridge University Press.

Reichenbach, H. (1938). Experience and Prediction. University of Chicago Press.

———. (1940). On the justification of induction. The Journal of Philosophy, 37, 97–103.

Salmon, W. C. (1963). On vindicating induction. Philosophy of Science, 30, 252–261.

———. (1966). The Foundations of Scientific Inference. University of Pittsburgh Press.

———. (1991). Hans Reichenbach’s vindication of induction. Erkenntnis, 35, 99–122.

Savage, L. J. (1954). The Foundations of Statistics. John Wiley & Sons.

Sinervo, P. (2002). Signal significance in particle physics. In M. Whalley & L. Lyons (Eds.), Proceedings of the Conference on Advanced Statistical Techniques in Particle Physics. Durham, UK: Institute of Particle Physics Phenomenology. https://arxiv.org/abs/hep-ex/0208005v1

———. (2003). Definition and treatment of systematic uncertainties in high energy physics and astrophysics. In Lyons L., Mount R., & R. Reitmeyer (Eds.), Proceedings of the Conference on Statistical Problems in Particle Physics, Astrophysics, and Cosmology (PhyStat2003) (pp. 122–129). Stanford Linear Accelerator Center. https://www.slac.stanford.edu/econf/C030908/papers/TUAT004.pdf

Venn, J. (1888). The Logic of Chance. London: MacMillan and Co. (Originally published in 1866).

Wald, A. (1943). Tests of statistical hypotheses concerning several parameters when the number of observations is large. Transactions of the American Mathematical Society, 54, 426–482.

Wasserman, L. (2003). All of Statistics: A Concise Course in Statistical Inference. Springer.

Wasserstein, R. L., & Lazar, N. A. (2016). The ASA’s statement on p-values: Context, process, and purpose. American Statistician, 70, 129–133.

Weintraub, R. (1995). What was Hume’s contribution to the problem of induction? The Philosophical Quarterly, 45, 460–470.

Wilks, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. The Annals of Mathematical Statistics, 9, 60–62.


  1. Hume (2007).

  2. Weintraub (1995).

  3. Reichenbach (1938) and Reichenbach (1940).

  4. Salmon (1963), Salmon (1966), Salmon (1991).

  5. Good (1988).

  6. Hacking (2001).

  7. Huber (2007).

  8. Cowan (1998) and Cowan (2016).

  9. Venn (1888)

  10. Fisher (1912).

  11. Fisher (1915).

  12. Berger (2003).

  13. Mayo (1996).

  14. Mayo (1981).

  15. Kendall (1946).

  16. James (2006).

  17. Cowan (1998) and Cowan (2016).

  18. Cranmer (2015).

  19. Neyman & Pearson (1933).

  20. Wilks (1938).

  21. Wald (1943).

  22. Sinervo (2002) and Cowan (2012).

  23. Feldman & Cousins (1998).

  24. Aldrich (1997).

  25. Fréchet (1943), Cramér (1946), Rao (1945), and Rao (1947).

  26. Cowan, Cranmer, Gross, & Vitells (2011).

  27. Sinervo (2003).

  28. Wasserstein & Lazar (2016).

  29. Benjamin, D.J. et al. (2017).

  30. Hastie, Tibshirani, & Friedman (2009).

  31. Leemis & McQueston (2008).

  32. Wasserman (2003).

  33. Savage (1954).