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Statistical and Physical Models

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Uncertainty

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Abstract

Statistical models are probability models and physical models are causal or deterministic or mixed causal-deterministic-probability models applied to observable propositions. It is observations which turn probability into statistics. Statistical and physical models are thus verifiable, and all use statistics in their verification. All models should be verified, but most aren’t. Classical modeling emphasizes hypothesis or “significance” testing and estimation. No hypothesis test, Bayesian or frequentist, should ever be used. Death to all p-values or Bayes factors! Hypothesis testing does not prove or show cause; therefore, embedded in every test used to claim cause is a fallacy. If cause is known, probability isn’t needed. Neither should parameter-centric (estimation, etc.) methods be used. Instead, use only probability, make probabilistic predictions of observables given observations and other premises, then verify these predictions. Measures of model goodness and observational relevance are given in a language which requires no sophisticated mathematical training to understand. Speak only in terms of observables and match models to measurement. Hypothesis-testing and parameter estimation are responsible for a pandemic of over-certainty in the sciences. Decisions are not probability, a fact with many consequences.

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Notes

  1. 1.

    The simplest example is a test for differences in proportion from two groups, where \(n_{1} = n_{2} = 1\) and where \(x_{1} = 1,x_{2} = 0\), or \(x_{1} = 0,x_{2} = 1\). Small “samples” frequently bust frequentist methods.

  2. 2.

    The data is available at http:\\wmbriggs.com\public\sat.csv.

References

  1. Agresti, A.: Categorical Data Analysis. Wiley, New York (2002)

    Book  MATH  Google Scholar 

  2. Aitchison, J.: Goodness of prediction fit. Biometrika 62, 547–554 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ando, T.: Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayesian models. Biometrika 94, 443–458 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Arjas, E., Andreev, A.: Predictive inference, causal reasoning, and model assessment in nonparametric Bayesian analysis. Lifetime Data Anal. 6, 187–205 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Armstrong, J.S.: Significance testing harms progress in forecasting (with discussion). Int. J. Forecast. 23, 321–327 (2007)

    Article  Google Scholar 

  6. Berger, J.: Statistical Decision Theory and Bayesian Analysis, 2nd edn. Springer, New York (2010)

    Google Scholar 

  7. Berger, J.O., Selke, T.: Testing a point null hypothesis: the irreconcilability of p-values and evidence. JASA 33, 112–122 (1987)

    MathSciNet  MATH  Google Scholar 

  8. Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. Wiley, New York (2000)

    MATH  Google Scholar 

  9. Blackwell, D., Girshick, M.: Theory of Games and Statistical Decisions. Dover, Mineola (1954)

    MATH  Google Scholar 

  10. Briggs, W.M.: On probability leakage. arxiv.org/abs/1201.3611 (2013)

    Google Scholar 

  11. Briggs, W.M.: The third way of probability & statistics: beyond testing and estimation to importance, relevance, and skill. arxiv.org/abs/1508.02384 (2015)

    Google Scholar 

  12. Briggs, W.M., Ruppert, D.: Assessing the skill of yes/no predictions. Biometrics 61 (3), 799–807 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Briggs, W.M., Zaretzki, R.A.: The skill plot: a graphical technique for evaluating continuous diagnostic tests. Biometrics 64, 250–263 (2008, with discussion)

    Google Scholar 

  14. Burnham, K.P., Anderson, D.R.: Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach, 2nd edn. Springer, New York (2002)

    MATH  Google Scholar 

  15. Christensen, R., Utts, J.: Bayesian resolution of the exchange paradox. Am. Stat. 46, 274–276 (1992)

    MathSciNet  Google Scholar 

  16. Cohen, J.: The earth is round (p < . 05). Am. Psychol. 49, 997–1003 (1994)

    Google Scholar 

  17. Colquhoun, D.: An investigation of the false discovery rate and the misinterpretation of p-values. R. Soc. Open Sci. 1, 1–16 (2014)

    Article  Google Scholar 

  18. Dawid, A.P.: Present position and potential developments: some personal views. J. R. Stat. Soc. A 147, 278–292 (1984)

    Article  MathSciNet  Google Scholar 

  19. Dawid, A.P., Vovk, V.: Prequential probability: principles and properties. Bernoulli 5, 125–162 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  20. Diaconis, P., Mosteller, F.: The analysis of sequential experiments with feedback to subjects. Ann. Stat. 9, 3–23 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  21. Dorigo, T.: The Jeffreys-Lindley paradox. Science 2.0. http://www.science20.com/quantum_diaries_survivor/jeffreyslindley_paradox-87184 (2012)

  22. Ellis, G., Silk, J.: Scientific method: defend the integrity of physics. Nature 516, 321–323 (2014)

    Article  Google Scholar 

  23. de Finetti, B.: Foresight: its logical laws, its subjective sources. In: Studies in Subjective Probability, 2nd edn. Krieger Publishing Company, Huntington (1980)

    Google Scholar 

  24. Fisher, R.: Statistical Methods for Research Workers, 14th edn. Oliver and Boyd, Edinburgh (1970)

    MATH  Google Scholar 

  25. Geisser, S.: On prior distributions for binary trials. Am. Stat. 38 (4), 244–247 (1984)

    MathSciNet  MATH  Google Scholar 

  26. Geisser, S.: Predictive Inference: An Introduction. Chapman & Hall, New York (1993)

    Book  MATH  Google Scholar 

  27. Gigerenzer, G.: Mindless statistics. J. Socio-Econ. 33, 587–606 (2004)

    Article  Google Scholar 

  28. Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. JASA 102, 359–378 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  29. Gneiting, T., Raftery, A.E., Balabdaoui, F.: Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. Ser. B: Stat. Methodol. 69, 243–268 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Henricha, J., Heinea, S.J., Norenzayana, A.: The weirdest people in the world? Behav. Brain Sci. 33, 61–83 (2010)

    Article  Google Scholar 

  31. Hersbach, H.: Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather Forecast. 15, 559–570 (2000)

    Article  Google Scholar 

  32. Ioannidis, J.P.: Why most published research findings are false. PLoS Med. 2 (8), e124 (2005)

    Article  MathSciNet  Google Scholar 

  33. Jaynes, E.T.: Making Decisions, 2nd edn. Wiley, New York (1985)

    Google Scholar 

  34. Jaynes, E.T.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  35. Johnson, W.O.: Predictive influence in the log normal survival model. In: Modelling and Prediction: Honoring Seymour Geisser, pp. 104–121. Springer, New York (1996)

    Google Scholar 

  36. Johnson, W.O., Geisser, S.: A predictive view of the detection and characterization of influence observations in regression analysis. JASA 78, 427–440 (1982)

    Google Scholar 

  37. Kullback, S.: Information Theory and Statistics. Dover, Mineola (1968)

    MATH  Google Scholar 

  38. Lee, J.C., Johnson, W.O., Zellner, A. (eds.): Modelling and Prediction: Honoring Seymour Geisser. Springer, New York (1996)

    MATH  Google Scholar 

  39. Little, R.: Calibrated Bayes: a Bayes/frequentist roadmap. Am. Stat. 60 (3), 1–11 (2006)

    Article  MathSciNet  Google Scholar 

  40. MacCoun, R., Perlmutter, S.: Blind Analysis as a Correction for Confirmatory Bias in Physics and in Psychology. In: Psychological Science Under Scrutiny: Recent Challenges and Proposed Solutions, pp. 589–612. Wiley, New York (2016)

    Google Scholar 

  41. Murphy, A.H.: Forecast verification: its complexity and dimensionality. Mon. Weather Rev. 119, 1590–1601 (1991)

    Article  Google Scholar 

  42. Murphy, A.H., Winkler, R.L.: A general framework for forecast verification. Mon. Weather Rev. 115, 1330–1338 (1987)

    Article  Google Scholar 

  43. Newman, J.H.C.: The Grammar of Ascent. Image Books, New York (1955)

    Google Scholar 

  44. Robert, C.: On the jeffreys-lindley’s paradox. arxiv.org/abs/stat.ME/1303.5973v3 (2013)

    Google Scholar 

  45. Robert, C.P.: The Bayesian Choice, 2nd edn. Springer, New York (2001)

    Google Scholar 

  46. Rucker, R.: Infinity and the Mind: The Science and Philosophy of the Infinite. Bantam, New York (1983)

    MATH  Google Scholar 

  47. Savage, L.: The Foundations of Statistics. Dover, Mineola (1972)

    MATH  Google Scholar 

  48. Schervish, M.: A general method for comparing probability assessors. Ann. Stat. 17, 1856–1879 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  49. Smith, R.L.: Bayesian and Frequentist Approaches to Parametric Predictive Inference (with Discussion). Bayesian Statistics, vol. 6, pp. 589–612. Oxford University Press, Oxford (1998)

    Google Scholar 

  50. Spiegelhalter, D.J., Best, N.G., Carlin, B.: Bayesian measures of model complexity and fit. Noûs 64, 583–639 (2002)

    MathSciNet  MATH  Google Scholar 

  51. Tetlock, P.E.: Expert Political Judgement. Princeton University Press, Princeton (2005)

    Google Scholar 

  52. West, M.: Bayesian model monitoring. J. R. Stat. Soc. B 48 (1), 70–78 (1986)

    MathSciNet  MATH  Google Scholar 

  53. Wilks, D.S.: Statistical Methods in the Atmospheric Sciences, 2nd edn. Academic, New York (2006)

    Google Scholar 

  54. Williamson, J.: In Defense of Objective Bayesianism. Oxford University Press, Oxford (2010)

    Book  MATH  Google Scholar 

  55. Ziliak, S.T., McCloskey, D.N.: The Cult of Statistical Significance. University of Michigan Press, Ann Arbor (2008)

    MATH  Google Scholar 

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  1. New York City, NY, USA

    William Briggs

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  1. William Briggs
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Briggs, W. (2016). Statistical and Physical Models. In: Uncertainty. Springer, Cham. https://doi.org/10.1007/978-3-319-39756-6_9

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