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General

Evidential Calibration of Confidence Intervals

ORCID Icon, ORCID Icon & ORCID Icon
Pages 47-57 | Received 16 Jan 2023, Accepted 14 May 2023, Published online: 26 Jun 2023

References

  • Amrhein, V., Trafimow, D., and Greenland, S. (2019), “Inferential Statistics as Descriptive Statistics: There is No Replication Crisis If We Don’t Expect Replication,” The American Statistician, 73, 262–270. DOI: 10.1080/00031305.2018.1543137.
  • Berger, J., Bayarri, M. J., and Pericchi, L. R. (2013), “The Effective Sample Size,” Econometric Reviews, 33, 197–217. DOI: 10.1080/07474938.2013.807157.
  • Berger, J. O., and Delampady, M. (1987), “Testing Precise Hypotheses,” Statistical Science 2, 317–335. DOI: 10.1214/ss/1177013238.
  • 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, 112–122. DOI: 10.2307/2289131.
  • Blume, J. D. (2002), “Likelihood Methods for Measuring Statistical Evidence,” Statistics in Medicine, 21, 2563–2599. DOI: 10.1002/sim.1216.
  • Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., and Knuth, D. E. (1996), “On the Lambert W Function,” Advances in Computational Mathematics, 5, 329–359. DOI: 10.1007/BF02124750.
  • Edwards, A. W. F. (1971). Likelihood, London: Cambridge University Press.
  • Edwards, W., Lindman, H., and Savage, L. J. (1963), “Bayesian Statistical Inference for Psychological Research,” Psychological Review, 70, 193–242. DOI: 10.1037/h0044139.
  • Fisher, R. A. (1956), Statistical Methods and Scientific Inference, Edinburgh: Oliver & Boyd.
  • Fong, E., and Holmes, C. C. (2020), “On the Marginal Likelihood and Cross-validation,” Biometrika, 107, 489–496. DOI: 10.1093/biomet/asz077.
  • Fraser, D. A. S. (2019), “The p-value Function and Statistical Inference,” The American Statistician, 73, 135–147. DOI: 10.1080/00031305.2018.1556735.
  • Gneiting, T., and Raftery, E. (2007), “Strictly Proper Scoring Rules, Prediction, and Estimation,” Journal of the American Statistical Association, 102, 359–377. DOI: 10.1198/016214506000001437.
  • Good, I. J. (1992), “The Bayes/non-Bayes Compromise: A Brief Review,” Journal of the American Statistical Association, 87, 597–606. DOI: 10.1080/01621459.1992.10475256.
  • Greenland, S. (2023), “Divergence versus Decision P-values: A Distinction Worth Making in Theory and Keeping in Practice: Or, How Divergence P-values Measure Evidence Even When Decision P-values Do Not,” Scandinavian Journal of Statistics, 50, 54–88. DOI: 10.1111/sjos.12625.
  • Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., and Altman, D. G. (2016), “Statistical Tests, P Values, Confidence Intervals, and Power: A Guide to Misinterpretations,” European Journal of Epidemiology, 31, 337–350. DOI: 10.1007/s10654-016-0149-3.
  • Grünwald, P., de Heide, R., and Koolen, W. (2019), “Safe Testing,” DOI: 10.48550/ARXIV.1906.07801., preprint.
  • Grünwald, P. (2023), “The E-posterior,” Philosophical Transactions of the Royal Society A, 381. DOI: 10.1098/rsta.2022.0146.
  • Hacking, I. (1965), Logic of Statistical Inference, New York: Cambridge University Press.
  • Held, L., and Ott, M. (2018), “On p-values and Bayes Factors,” Annual Review of Statistics and Its Application, 5, 393–419. DOI: 10.1146/annurev-statistics-031017-100307.
  • Hendriksen, A., de Heide, R., and Grünwald, P. (2021), “Optional Stopping with Bayes Factors: A Categorization and Extension of Folklore Results, with an Application to Invariant Situations,” Bayesian Analysis, 16, 961–989. DOI: 10.1214/20-BA1234.
  • Hoekstra, R., Morey, R. D., Rouder, J. N., and Wagenmakers, E.-J. (2014), “Robust Misinterpretation of Confidence Intervals,” Psychonomic Bulletin & Review volume, 21, 1157–1164. DOI: 10.3758/s13423-013-0572-3.
  • Howard, S. R., Ramdas, A., McAuliffe, J., and Sekhon, J. (2021), “Time-Uniform, Nonparametric, Nonasymptotic Confidence Sequences,” The Annals of Statistics, 49, 1055–1080. DOI: 10.1214/20-AOS1991.
  • Jeffreys, H. (1961), Theory of Probability (3rd ed.), Oxford: Clarendon Press.
  • 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. DOI: 10.1111/j.1467-9868.2009.00730.x.
  • Kass, R. E., and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795. DOI: 10.1080/01621459.1995.10476572.
  • Kass, R. E., and Wasserman, L. (1995), “A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion,” Journal of the American Statistical Association, 90, 928–934. DOI: 10.1080/01621459.1995.10476592.
  • Lai, T. L. (1976), “On Confidence Sequences,” The Annals of Statistics, 4, 265–280. DOI: 10.1214/aos/1176343406.
  • Lindon, M., and Malek, A. (2020), “Sequential Testing of Multinomial Hypotheses with Applications to Detecting Implementation Errors and Missing Data in Randomized Experiments,” available at https://arxiv.org/abs/2011.03567v1.
  • Ly, A., Marsman, M., Verhagen, J., Grasman, R. P., and Wagenmakers, E.-J. (2017), “A Tutorial on Fisher Information,” Journal of Mathematical Psychology, 80, 40–55. DOI: 10.1016/j.jmp.2017.05.006.
  • O’Hagan, A., and Forster, J. J. (2004), Kendall’s Advanced Theory of Statistics, volume 2B: Bayesian Inference (2nd ed.), London, UK: Arnold.
  • Pace, L., and Salvan, A. (2020), “Likelihood, Replicability and Robbins’ Confidence Sequences,” International Statistical Review, 88, 599–615. DOI: 10.1111/insr.12355.
  • Pramanik, S., and Johnson, V. E. (2022), “Efficient Alternatives for Bayesian Hypothesis Tests in Psychology,” Psychological Methods. DOI: 10.1037/met0000482.
  • R Core Team (2023), R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
  • Rafi, Z., and Greenland, S. (2020), “Semantic and Cognitive Tools to Aid Statistical Science: Replace Confidence and Significance by Compatibility and Surprise,” BMC Medical Research Methodology, 20, 244. DOI: 10.1186/s12874-020-01105-9.
  • Raftery, A. E. (1999), “Bayes Factors and BIC,” Sociological Methods & Research, 27, 411–427. DOI: 10.1177/0049124199027003005.
  • RECOVERY Collaborative Group. (2021), “Dexamethasone in Hospitalized Patients with Covid-19,” New England Journal of Medicine, 384, 693–704. DOI: 10.1056/nejmoa2021436.
  • Robbins, H. (1970), “Statistical Methods Related to the Law of the Iterated Logarithm,” The Annals of Mathematical Statistics, 41, 1397–1409. DOI: 10.1214/aoms/1177696786.
  • Royall, R. (1997), Statistical Evidence: A Likelihood Paradigm, London; New York: Chapman & Hall.
  • Sellke, T., Bayarri, M. J., and Berger, J. O. (2001), “Calibration of p Values for Testing Precise Null Hypotheses,” The American Statistician, 55, 62–71. DOI: 10.1198/000313001300339950.
  • Shafer, G. (2021), “Descriptive Probability,” working paper #59 (version September 30, 2021). Available at http://probabilityandfinance.com/articles/59.pdf.
  • Spiegelhalter, D. J., Abrams, R., and Myles, J. P. (2004), Bayesian Approaches to Clinical Trials and Health-Care Evaluation, New York: Wiley.
  • Vovk, V. G. (1993), “A Logic of Probability, With Application to the Foundations of Statistics,” Journal of the Royal Statistical Society, Series B, 55, 317–341. DOI: 10.1111/j.2517-6161.1993.tb01904.x.
  • Wagenmakers, E.-J. (2022), “Approximate Objective Bayes Factors from P-values and Sample Size: The 3pn Rule,” DOI: 10.31234/osf.io/egydq.
  • Wagenmakers, E.-J., Gronau, Q. F., Dablander, F., and Etz, A. (2022), “The Support Interval,” Erkenntnis, 87, 589–601. DOI: 10.1007/s10670-019-00209-z.
  • Wagenmakers, E.-J., and Ly, A. (2023), “History and Nature of the Jeffreys-Lindley Paradox,” Archive for History of Exact Sciences, 77, 25–72. DOI: 10.1007/s00407-022-00298-3.
  • Wassmer, G., and Brannath, W. (2016), Group Sequential and Confirmatory Adaptive Designs in Clinical Trials, Cham: Springer. DOI: 10.1007/978-3-319-32562-0.