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Bayesian Versus Frequentist Inference

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Bayesian Evaluation of Informative Hypotheses

Part of the book series: Statistics for Social and Behavioral Sciences ((SSBS))

Abstract

Throughout this book, the topic of order restricted inference is dealt with almost exclusively from a Bayesian perspective. Some readers may wonder why the other main school for statistical inference – frequentist inference – has received so little attention here. Isn’t it true that in the field of psychology, almost all inference is frequentist inference?

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References

  1. Abelson, R.P.: On the surprising longevity of flogged horses: Why there is a case for the significance test. Psychological Science, 8, 12–15 (1997)

    Article  Google Scholar 

  2. Anscombe, F.J.: Sequential medical trials. Journal of the American Statistical Association, 58, 365–383 (1963)

    Article  MathSciNet  Google Scholar 

  3. Bakan, D.: The test of significance in psychological research. Psychological Bulletin, 66, 423–437 (1966)

    Article  Google Scholar 

  4. Barnard, G.A.: The meaning of a significance level. Biometrika, 34, 179–182 (1947)

    MATH  MathSciNet  Google Scholar 

  5. Basu, D.: On the elimination of nuisance parameters. Journal of the American Statistical Association, 72, 355–366 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  6. Batchelder, W.H.: Cognitive psychometrics: Combining two psychological traditions. CSCA Lecture, Amsterdam, The Netherlands, October 2007.

    Google Scholar 

  7. Berger, J.O.: Statistical Decision Theory and Bayesian Analysis (2nd ed.). New York, Springer (1985)

    MATH  Google Scholar 

  8. Berger, J.O.: Robust Bayesian analysis: Sensitivity to the prior. Journal of Statistical Planning and Inference, 25, 303–328 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. Berger, J.O., Berry, D.A.: The relevance of stopping rules in statistical inference. In: Gupta, S.S., Berger, J.O. (eds) Statistical Decision Theory and Related Topics: Vol. 1. New York, Springer (1988)

    Google Scholar 

  11. Berger, J.O., Berry, D.A.: Statistical analysis and the illusion of objectivity. American Scientist, 76, 159–165 (1988)

    Google Scholar 

  12. Berger, J.O., Liseo, B., Wolpert, R.L.: Integrated likelihood methods for eliminating nuisance parameters. Statistical Science, 14, 1–28 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  13. Berger, J.O., Pericchi, L.R.: The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109–122 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  14. Berger, J.O., Wolpert, R.L.: The Likelihood Principle. Institute of Mathematical Statistics (2nd ed.), Hayward, CA (1988)

    Google Scholar 

  15. Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. New York, Wiley (1994)

    Book  MATH  Google Scholar 

  16. Bowers, J.S., Vigliocco, G., Haan, R.: Orthographic, phonological, and articulatory contributions to masked letter and word priming. Journal of Experimental Psychology: Human Perception and Performance, 24, 1705–1719 (1998)

    Article  Google Scholar 

  17. Burdette, W.J., Gehan, E.A.: Planning and Analysis of Clinical Studies. Charles C. Springfield, IL, Thomas (1970)

    Google Scholar 

  18. Christensen, R.: Testing Fisher, Neyman, Pearson, and Bayes. The American Statistician, 59, 121–126 (2005)

    Article  MathSciNet  Google Scholar 

  19. Cox, D.R.: Some problems connected with statistical inference. The Annals of Mathematical Statistics, 29, 357–372 (1958)

    Article  MATH  Google Scholar 

  20. Cox, R.T.: Probability, frequency and reasonable expectation. American Journal of Physics, 14, 1–13 (1946)

    Article  MATH  MathSciNet  Google Scholar 

  21. Dawid, A.P.: Statistical theory: The prequential approach. Journal of the Royal Statistical Society, Series A, 147, 278–292 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  22. De Finetti, B.: Theory of Probability, Vols. 1 and 2. New York, Wiley (1974)

    Google Scholar 

  23. DeGroot, M.-H.: Optimal Statistical Decisions. New York, McGraw-Hill (1970)

    MATH  Google Scholar 

  24. Dennis, S., Humphreys, M.S.: A context noise model of episodic word recognition. Psychological Review, 108, 452–477 (2001)

    Article  Google Scholar 

  25. Dickey, J.M.: Scientific reporting and personal probabilities: Student’s hypothesis. Journal of the Royal Statistical Society, Series B, 35, 285–305 (1973)

    MathSciNet  Google Scholar 

  26. Edwards, W., Lindman, H., Savage, L.J.: Bayesian statistical inference for psychological research. Psychological Review, 70, 193–242 (1963)

    Article  Google Scholar 

  27. Efron, B.: Why isn’t everyone a Bayesian? The American Statistician, 40, 1–5 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  28. Estes, W.K.: The problem of inference from curves based on group data. Psychological Bulletin, 53, 134–140 (1956)

    Article  Google Scholar 

  29. Estes, W.K.: Traps in the route to models of memory and decision. Psychonomic Bulletin & Review, 9, 3–25 (2002)

    Google Scholar 

  30. Fishburn, P.C.: The axioms of subjective probability. Statistical Science, 1, 335–345 (1986)

    Article  MathSciNet  Google Scholar 

  31. Fisher, R.A.: Statistical Methods for Research Workers (5th ed.). London, Oliver and Boyd (1934)

    Google Scholar 

  32. Fisher, R.A.: Statistical Methods for Research Workers (13th ed.). New York, Hafner (1958)

    Google Scholar 

  33. Forster, K.I., Mohan, K., Hector, J.: The mechanics of masked priming. In: Kinoshita, S., Lupker, S.J. (eds) Masked Priming: The State of the Art. New York, Psychology Press (2003)

    Google Scholar 

  34. Galavotti, M.C.: A Philosophical Introduction to Probability. Stanford, CA, CSLI Publications (2005)

    Google Scholar 

  35. Gelfand, A.E., Smith, A.F.M., Lee, T. M.: Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. Journal of the American Statistical Association, 87, 523–532 (1992)

    Article  MathSciNet  Google Scholar 

  36. Gelman, A., Hill, J.: Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge, Cambridge University Press (2007)

    Google Scholar 

  37. Gigerenzer, G.: The superego, the ego, and the id in statistical reasoning. In: Keren, G., Lewis, C. (eds) A Handbook for Data Analysis in the Behavioral Sciences: Methodological Issues. Hillsdale, NJ, Erlbaum (1993)

    Google Scholar 

  38. Gigerenzer, G.: We need statistical thinking, not statistical rituals. Behavioral and Brain Sciences, 21, 199–200 (1998)

    Article  Google Scholar 

  39. Gigerenzer, G.: Mindless statistics. The Journal of Socio–Economics, 33, 587–606 (2004)

    Google Scholar 

  40. Gigerenzer, G., Krauss, S., Vitouch, O.: The null ritual: What you always wanted to know about significance testing but were afraid to ask. In: Kaplan, D. (ed) The Sage Handbook of Quantitative Methodology for the Social Sciences. Thousand Oaks, CA, Sage (2004)

    Google Scholar 

  41. Gill, J.: Bayesian Methods: A Social and Behavioral Sciences Approach. Boca Raton, FL, CRC Press (2002).

    MATH  Google Scholar 

  42. Good, I.J.: Weight of evidence: A brief survey. In: Bernardo, J.M., DeGroot, M.-H., Lindley, D.V., Smith, A.F.M. (eds) Bayesian Statistics 2. New York, Elsevier (1985)

    Google Scholar 

  43. Goodman, S.N.: P values, hypothesis tests, and likelihood: Implications for epidemiology of a neglected historical debate. American Journal of Epidemiology, 137, 485–496 (1993)

    Google Scholar 

  44. Haller, H., Krauss, S.: Misinterpretations of significance: A problem students share with their teachers? Methods of Psychological Research, 7, 1–20 (2002)

    Google Scholar 

  45. Heathcote, A., Brown, S., Mewhort, D.J.K.: The power law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review, 7, 185–207 (2000)

    Google Scholar 

  46. Hoffman, L., Rovine, M.J.: Multilevel models for the experimental psychologist: Foundations and illustrative examples. Behavior Research Methods, 39, 101–117 (2007)

    Google Scholar 

  47. Hoijtink, H.: Confirmatory latent class analysis: Model selection using Bayes factors and (pseudo) likelihood ratio statistics. Multivariate Behavioral Research, 36, 563–588 (2001)

    Article  Google Scholar 

  48. Howson, C., Urbach, P.: Scientific Reasoning: The Bayesian Approach (3rd ed.). Chicago, Open Court (2006)

    Google Scholar 

  49. Hubbard, R., Bayarri, M.J.: Confusion over measures of evidence (p’s) versus errors (α’s) in classical statistical testing. The American Statistician, 57, 171–182 (2003)

    Article  MathSciNet  Google Scholar 

  50. Huntjens, R.J.C., Peters, M.L., Woertman, L., Bovenschen, L.M., Martin, R.C., Postma, A.: Inter-identity amnesia in dissociative identity disorder: A simulated memory impairment? Psychological Medicine, 36, 857–863 (2006)

    Article  Google Scholar 

  51. Jaynes, E.T.: Prior probabilities. IEEE Transactions on Systems Science and Cybernetics, 4, 227–241 (1968)

    Article  Google Scholar 

  52. Jaynes, E.T.: Confidence intervals vs Bayesian intervals. In: Harper, W.L., Hooker, C.A. (eds) Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. 2. Dordrecht, Reidel (1976)

    Google Scholar 

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

    MATH  Google Scholar 

  54. Jeffreys, H.: On the relation between direct and inverse methods in statistics. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 160, 325–348 (1937)

    Google Scholar 

  55. Jeffreys, H.: Theory of Probability. Oxford, Oxford University Press (1961)

    MATH  Google Scholar 

  56. Kass, R.E., Raftery, A.E.: Bayes factors. Journal of the American Statistical Association, 90, 377–395 (1995)

    Google Scholar 

  57. Kass, R.E., Wasserman, L.: A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association, 90, 928–934 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  58. Kass, R.E., Wasserman, L.: The selection of prior distributions by formal rules. Journal of the American Statistical Association, 91, 1343–1370 (1996)

    Article  MATH  Google Scholar 

  59. Klugkist, I., Kato, B., Hoijtink, H.: Bayesian model selection using encompassing priors. Statistica Neerlandica, 59, 57–69 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  60. Klugkist, I., Laudy, O., Hoijtink, H.: Inequality constrained analysis of variance: A Bayesian approach. Psychological Methods, 10, 477–493 (2005)

    Article  Google Scholar 

  61. Klugkist, I., Laudy, O., Hoijtink, H.: Bayesian eggs and Bayesian omelettes: Reply to Stern (2005). Psychological Methods, 10, 500–503 (2005)

    Article  Google Scholar 

  62. Laudy, O., Zoccolillo, M., Baillargeon, R.H., Boom, J., Tremblay, R.E., Hoijtink, H.: Applications of confirmatory latent class analysis in developmental psychology. European Journal of Developmental Psychology, 2, 1–15 (2005)

    Article  Google Scholar 

  63. Lee, M.D., Webb, M.R.: Modeling individual differences in cognition. Psychonomic Bulletin & Review, 12, 605–621 (2005)

    Google Scholar 

  64. Lindley, D. V.: A statistical paradox. Biometrika, 44, 187–192 (1957)

    MATH  MathSciNet  Google Scholar 

  65. Lindley, D.V.: Bayesian Statistics, a Review. Philadelphia, PA, SIAM (1972)

    Google Scholar 

  66. Lindley, D.V.: Scoring rules and the inevitability of probability. International Statistical Review, 50, 1–26 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  67. Lindley, D.V.: The analysis of experimental data: The appreciation of tea and wine. Teaching Statistics, 15, 22–25 (1993)

    Article  Google Scholar 

  68. Lindley, D.V.: The philosophy of statistics. The Statistician, 49, 293–337 (2000)

    Google Scholar 

  69. Lindley, D.V., Scott, W.F.: New Cambridge Elementary Statistical Tables. London, Cambridge University Press (1984)

    MATH  Google Scholar 

  70. MacKay, D.J.C.: Information Theory, Inference, and Learning Algorithms. Cambridge, Cambridge University Press (2003)

    MATH  Google Scholar 

  71. Morey, R.D., Pratte, M.S., Rouder, J.N.: Problematic effects of aggregation in zROC analysis and a hierarchical modeling solution. Journal of Mathematical Psychology (in press)

    Google Scholar 

  72. Morey, R.D., Rouder, J.N., Speckman, P.L.: A statistical model for discriminating between subliminal and near-liminal performance. Journal of Mathematical Psychology, 52, 21–36 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  73. Myung, I.J., Forster, M.R., Browne, M.W.: Model selection [Special issue]. Journal of Mathematical Psychology, 44(1–2) (2000)

    Article  Google Scholar 

  74. Navarro, D.J., Griffiths, T.L., Steyvers, M., Lee, M.D.: Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology, 50, 101–122 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  75. Nelson, N., Rosenthal, R., Rosnow, R.L.: Interpretation of significance levels and effect sizes by psychological researchers. American Psychologist, 41, 1299–1301 (1986)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  77. O’Hagan, A.: Fractional Bayes factors for model comparison. Journal of the Royal Statistical Society, Series B, 57, 99–138 (1997)

    MathSciNet  Google Scholar 

  78. O’Hagan, A.: Dicing with the unknown. Significance, 1, 132–133 (2004)

    Article  MathSciNet  Google Scholar 

  79. O’Hagan, A., Forster, J.: Kendall’s Advanced Theory of Statistics Vol. 2B: Bayesian Inference (2nd ed.). London, Arnold (2004)

    Google Scholar 

  80. Peto, R., Pike, M.C., Armitage, P., Breslow, N.E., Cox, D.R., Howard, S.V., Mantel, N., McPherson, K., Peto, J., Smith, P.G.: Design and analysis of randomized clinical trials requiring prolonged observation of each patient, I: Introduction and design. British Journal of Cancer, 34, 585–612 (1976)

    Google Scholar 

  81. Pocock, S.J.: Group sequential methods in the design and analysis of clinical trials. Biometrika, 64, 191–199 (1977)

    Article  Google Scholar 

  82. Raftery, A.E.: Bayesian model selection in social research. In: Marsden, P.V. (ed) Sociological Methodology. Cambridge, Blackwells (1995)

    Google Scholar 

  83. Ramsey, F.P.: Truth and probability. In: Braithwaite, R.B. (ed) The Foundations of Mathematics and Other Logical Essays. London, Kegan Paul (1926)

    Google Scholar 

  84. Rosenthal, R., Gaito, J.: The interpretation of levels of significance by psychological researchers. The Journal of Psychology, 55, 33–38 (1963)

    Google Scholar 

  85. Rosnow, R.L., Rosenthal, R.: Statistical procedures and the justification of knowledge in psychological science. American Psychologist, 44, 1276–1284 (1989)

    Article  Google Scholar 

  86. Rouder, J.N., Lu, J.: An introduction to Bayesian hierarchical models with an application in the theory of signal detection. Psychonomic Bulletin & Review, 12, 573–604 (2005)

    Google Scholar 

  87. Rouder, J.N., Lu, J., Morey, R.D., Sun, D., Speckman, P.L.: A hierarchical process dissociation model. Journal of Experimental Psychology: General (in press)

    Google Scholar 

  88. Rouder, J.N., Lu, J., Speckman, P.L., Sun, D., Jiang, Y.: A hierarchical model for estimating response time distributions. Psychonomic Bulletin & Review, 12, 195–223 (2005)

    Google Scholar 

  89. Rouder, J.N., Lu, J., Sun, D., Speckman, P., Morey, R., Naveh-Benjamin, M.: Signal detection models with random participant and item effects. Psychometrika (in press)

    Google Scholar 

  90. Royall, R.: The effect of sample size on the meaning of significance tests. The American Statistician, 40, 313–315 (1986)

    Article  MATH  Google Scholar 

  91. Royall, R.M.: Statistical Evidence: A Likelihood Paradigm. London, Chapman & Hall (1997)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  93. Savage, L.J.: The foundations of statistics reconsidered. In: Neyman, J. (ed) Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1. Berkely, CA, University of California Press (1961)

    Google Scholar 

  94. Smith, A.F.M., Roberts, G.O.: Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B, 55, 3–23 (1993)

    MATH  MathSciNet  Google Scholar 

  95. Spiegelhalter, D.J., Thomas, A., Best, N., Lunn, D.: WinBUGS Version 1.4 User Manual. Medical Research Council Biostatistics Unit, Cambridge (2003)

    Google Scholar 

  96. Stuart, A., Ord, J.K., Arnold, S.: Kendall’s Advanced Theory of Statistics Vol. 2A: Classical Inference & the Linear Model (6th ed.). London, Arnold (1999)

    Google Scholar 

  97. Wagenmakers, E.-J.: A practical solution to the pervasive problems of p values. Psychonomic Bulletin & Review, 14, 779–804 (2007)

    Google Scholar 

  98. Wagenmakers, E.-J., Grünwald, P.: A Bayesian perspective on hypothesis testing. Psychological Science, 17, 641–642 (2006)

    Article  Google Scholar 

  99. Wagenmakers, E.-J., Grünwald, P., Steyvers, M.: Accumulative prediction error and the selection of time series models. Journal of Mathematical Psychology, 50, 149–166 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  100. Wagenmakers, E.-J., Waldorp, L.: Model selection: Theoretical developments and applications [Special issue]. Journal of Mathematical Psychology, 50, 99–214 (2006)

    Article  MathSciNet  Google Scholar 

  101. Wasserman, L.: All of Statistics: A Concise Course in Statistical Inference. New York, Springer (2004)

    MATH  Google Scholar 

  102. Wilkinson, L., the Task Force on Statistical Inference: Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594–604 (1999)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Psychology, University of Amsterdam, Roetersstraat 15, 1018 WB, Amsterdam, the Netherlands

    Eric-Jan Wagenmakers

  2. Department of Cognitive Sciences, University of California at Irvine, 3151 Social Science Plaza, Irvine, CA, 92697, USA

    Michael Lee & Geoffrey J. Iverson

  3. Department of Quantitative and Personality Psychology, University of Leuven, Tiensestraat 102, 3000, Leuven, Belgium

    Tom Lodewyckx

Authors
  1. Eric-Jan Wagenmakers
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  2. Michael Lee
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  3. Tom Lodewyckx
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  4. Geoffrey J. Iverson
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Correspondence to Eric-Jan Wagenmakers .

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Editors and Affiliations

  1. Department of Methods and Statistics, Faculty of Social Sciences, University of Utrecht, P.O. Box 80140, 3508 TC, Utrecht, The Netherlands

    Herbert Hoijtink  & Irene Klugkist  & 

  2. Department of Clinical and Health Psychology, Faculty of Social Sciences, University of Utrecht, P.O. Box 80140, 3508 TC, Utrecht, The Netherlands

    Paul A. Boelen

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Wagenmakers, EJ., Lee, M., Lodewyckx, T., Iverson, G.J. (2008). Bayesian Versus Frequentist Inference. In: Hoijtink, H., Klugkist, I., Boelen, P.A. (eds) Bayesian Evaluation of Informative Hypotheses. Statistics for Social and Behavioral Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-09612-4_9

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