796
Views
5
CrossRef citations to date
0
Altmetric
STATISTICAL PRACTICE

Comparing Objective and Subjective Bayes Factors for the Two-Sample Comparison: The Classification Theorem in Action

, , &
Pages 22-31 | Received 01 Apr 2016, Accepted 01 Apr 2017, Published online: 10 May 2018

References

  • Bartlett, M. S. (1957), “A Comment on D. V. Lindley's Statistical Paradox,” Biometrika, 44, 533–534.
  • Bayarri, M.J., Berger, J.O., Forte, A., and García-Donato, G. (2012), “Criteria for Model Choice with Application to Variable Selection,” The Annals of Statistics, 40, 1550–1577.
  • Bem, D. J. (2011), “Feeling the Future: Experimental Evidence for Anomalous Retroactive Influences on Cognition and Affect,” Journal of Personality and Social Psychology, 100, 407–425.
  • Bem, D. J., Utts, J. M., and Johnson, W. O. (2011), “Must Psychologists Change the Way They Analyze Their Data? A Response to Wagenmakers, Wetzels, Borsboom and Van der Mass,” Journal of Personality and Social Psychology, 101, 716–719.
  • Benjamini, Y., and Braun, H. (2002), “John W. Tukey's Contributions to Multiple Comparisons,” The Annals of Statistics 30, 1576–1594.
  • Berger, J. O., and Delampady, M. (1987), “Testing Precise Hypotheses,” Statistical Science 2, 317–335.
  • Berger, J. O., and Pericchi, L. R. (1996), “The Intrinsic Bayes Factor for Model Selection and Prediction,” Journal of the American Statistical Association, 91, 109–122
  • ——— (2001), “Objective Bayesian Methods for Model Selection: Introduction and Comparison,” in Model Selection, Beachwood, OH: Institute of Mathematical Statistics, 135–207.
  • Berger, J. O., and Sellke, T. (1987), “Testing a Point Null Hypothesis: The Irreconcilability of p values and Evidence,” Journal of the American Statistical Association, 82, 112–139.
  • Ben-Zvi, D., and Makar, K. (2016), The Teaching and Learning of Statistics: International Perspectives, New York: Springer.
  • Do, K. A., Müller, P., and Vannucci, M. (2012), Bayesian Inference for Gene Expression and Proteomics, New York: Cambridge University Press.
  • Efron, B. (2010), Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction, New York: Cambridge University Press.
  • Fox, R. J., and Dimmic, M. W. (2006), “A Two-Sample Bayesian t-test for Microarray Data,” BMC Bioinformatics, 7, 126, doi:10.1186/1471-2105-7-126.
  • Gönen, M., Johnson, W. O., Lu, Y., and Westfall, P. H. (2005), “The Bayesian Two-Sample t Test,” The American Statistician, 59, 252–257.
  • Guindani, M, Müller, P., and Zhang, S. (2009), “A Bayesian Discovery Procedure,” Journal of the Royal Statistical Society, Series B, 71, 905–925.
  • Held, L. and Ott, M. (2016), “How the Maximal Evidence of p-values Against Point Null Hypotheses Depends on Sample Size,” The American Statistician, 70, 335–341.
  • Jeffreys, H. (1961), Theory of Probability, Oxford, UK: Oxford University Press.
  • Johnson, V. E. (2013a), “Uniformly Most Powerful Bayesian Tests,” Annals of Statistics 41, 1715–1741.
  • ——— (2013b), “Revised Standards for Statistical Evidence,” Proceedings of the National Academy of Sciences of the United States of America, 110, 19313–19317.
  • Johnson, V.E., and Rossell, D. (2010), “On the Use of Non-Local Prior Densities in Bayesian Hypothesis Tests,” Journal of the Royal Statistical Society, Series B, 72, 143–170.
  • Jones, G., and Johnson, W. O. (2014), “Prior Elicitation: Interactive Spreadsheet Graphics with Sliders Can be Fun, and Informative,” The American Statistician 68, 42–51.
  • Kass, R. E., and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795.
  • Kleiner, I., and Movshovitz-Hadar, N. (1994), “The Role of Paradoxes in the Evolution of Mathematics,” The American Mathematical Monthly, 101, 963–974.
  • Kuhn, M., and Johnson, K. (2013), Applied Predictive Modeling, New York: Springer.
  • Liang, F., Paulo, R., Molina, G., Clyde, M. A., and Berger, J. O. (2008), “Mixtures of g Priors for Bayesian Variable Selection,” Journal of the American Statistical Association, 103, 410–423.
  • Masson, M. E. (2011), “A Tutorial on a Practical Bayesian Alternative to Null-Hypothesis Significance Testing,” Behavior Research Methods, 43, 679–690.
  • Mossbridge, J., Tressoldi, P., and Utts, J. (2011), “Physiological Anticipation of Unpredictable Stimuli: A Meta-Analysis,” unpublished manuscript.
  • Open Science Collaboration (2015), “Estimating the Reproducibility of Psychological Science,” Science, 349, aac4716. DOI: 10.1126/science.aac4716.
  • Rivera, I. A. (2011), “The Objective and Robust Student's t Test,” Unpublished presentation, Department of Mathematics, University of Puerto Rico, available at http://www.pericchi.info/content.html?content=D0A089CD92FAF37DC1E6B3CB951AE92D.
  • Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., and Iverson, G. (2009), “Bayesian t Tests for Accepting and Rejecting the Null Hypothesis,” Psychonomic Bulletin & Review, 16, 225–237.
  • Shaffer, J. P. (1999), “A Semi-Bayesian Study of Duncan's Bayesian Multiple Comparison Procedure,” Journal of Statistical Planning and Inference, 82, 197–213.
  • Shahbaba, B., and Johnson. W. O. (2013), “Bayesian Nonparametric Variable Selection as an Exploratory Tool for Discovering Differentially Expressed Genes,” Statistics in Medicine, 32, 2114–2126.
  • Utts, J., Norris, M., Suess, E., and Johnson, W. O. (2010), “The Strength of Evidence Versus the Power of Belief: Are We All Bayesians?,” in C. Reading ( Ed.), Data and Context in Statistics Education: Towards an Evidence-Based Society, Proceedings of the Eighth International Conference on Teaching Statistics ( ICOTS8, July, 2010), Ljubljana, Slovenia. Voorburg, The Netherlands: International Statistical Institute.
  • Wagenmakers, E. J. (2007), “A Practical Solution to the Pervasive Problems of p Values,” Psychonomic Bulletin & Review, 14, 779–804.
  • Wagenmakers, E. J., Wetzels, R., Borsboom, D., and van der Maas, H. (2011), “Why Psychologists Must Change the Way They Analyze Their Data: The Case of Psi,” Journal of Personality and Social Psychology, 100, 426–432.
  • Wang, M., and Liu, G. (2015), “A Simple Two-Sample Bayesian t-Test for Hypothesis Testing,” The American Statistician, 70, 195–201.
  • Wasserstein, R. L., and Lazar, N. A. (2016), “The ASA's Statement on p-Values: Context, Process, and Purpose,” The American Statistician, 70, 129–133.
  • Wetzels, R., Matzke, D., Lee, M. D., Rouder, J. N., Iverson, G. J., and Wagenmakers, E. -J. (2011), “Statistical Evidence in Experimental Psychology: An Empirical Comparison Using 855 t Tests,” Perspectives on Psychological Science, 6, 291–298.
  • Zellner, A., and Siow, A. (1980), “Posterior Odds Ratio for Selected Regression Hypotheses,” in Bayesian Statistics 1, 585–603, Valencia University Press.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.