The Support Interval

Annalen der Philosophie - Tập 87 - Trang 589-601 - 2020
Eric-Jan Wagenmakers1, Quentin F. Gronau1, Fabian Dablander1, Alexander Etz2
1Department of Psychology, University of Amsterdam, Amsterdam, The Netherlands
2University of California, Irvine, USA

Tóm tắt

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley’s paradox and provides an evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval.

Tài liệu tham khảo

Bartlett, M. S. (1957). A comment on D. V. Lindley’s statistical paradox. Biometrika, 44, 533–534.

Baskurt, Z., Evans, M., et al. (2013). Hypothesis assessment and inequalities for bayes factors and relative belief ratios. Bayesian Analysis, 8(3), 569–590.

Carnap, R. (1950). Logical foundations of probability. Chicago: The University of Chicago Press.

Cumming, G. (2014). The new statistics: Why and how. Psychological Science, 25, 7–29.

DeGroot, M. H. (1982). Lindley’s paradox: Comment. Journal of the American Statistical Association, 77, 336–339.

Dickey, J. M. (1971). The weighted likelihood ratio, linear hypotheses on normal location parameters. The Annals of Mathematical Statistics, 42, 204–223.

Dickey, J. M., & Lientz, B. P. (1970). The weighted likelihood ratio, sharp hypotheses about chances, the order of a Markov chain. The Annals of Mathematical Statistics, 41, 214–226.

Edwards, A. W. F. (1992). Likelihood. Baltimore, MD: The Johns Hopkins University Press.

Etz, A. (2018). Introduction to the concept of likelihood and its applications. Advances in Methods and Practices in Psychological Science, 1, 60–69.

Etz, A., & Wagenmakers, E.-J. (2017). J. B. S. Haldane’s contribution to the Bayes factor hypothesis test. Statistical Science, 32, 313–329.

Evans, M. (1997). Bayesian inference procedures derived via the concept of relative surprise. Communications in Statistics—Theory and Methods, 26, 1125–1143.

Evans, M. (2015). Measuring statistical evidence using relative belief. Boca Raton, FL: CRC Press.

Evans, M., & Tomal, J. (2018). Measuring statistical evidence and multiple testing. FACETS, 3(1), 563–583.

Haldane, J. B. S. (1932). A note on inverse probability. Mathematical Proceedings of the Cambridge Philosophical Society, 28, 55–61.

Heck, D. (2018). A caveat on the Savage–Dickey density ratio: The case of computing Bayes factors for regression parameters. PsyArXiv preprint. https://doi.org/10.31234/osf.io/7dzsj

Hudson, D. J. (1971). Interval estimation from the likelihood function. Journal of the Royal Statistical Society Series B (Methodological), 33, 256–262.

Jeffreys, H. (1939). Theory of probability (1st ed.). Oxford: Oxford University Press.

Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90, 773–795.

Keynes, J. M. (1921). A treatise on probability. London: Macmillan & Co.

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

Liu, C. C., & Aitkin, M. (2008). Bayes factors: Prior sensitivity and model generalizability. Journal of Mathematical Psychology, 52, 362–375.

Marin, J.-M., & Robert, C. P. (2010). On resolving the Savage–Dickey paradox. Electronic Journal of Statistics, 4, 643–654.

Morey, R. D., Romeijn, J. W., & Rouder, J. N. (2016). The philosophy of Bayes factors and the quantification of statistical evidence. Journal of Mathematical Psychology, 72, 6–18.

Natrella, M. G. (1960). The relation between confidence intervals and tests of significance: A teaching aid. The American Statistician, 14, 20–22.

Robert, C. P. (2014). On the Jeffreys–Lindley paradox. Philosophy of Science, 81(2), 216–232.

Rouder, J. N., Haaf, J. M., & Vandekerckhove, J. (2018). Bayesian inference for psychology, part IV: Parameter estimation and Bayes factors. Psychonomic Bulletin & Review, 25, 102–113.

Rouder, J. N., & Morey, R. D. (2019). Teaching Bayes’ theorem: Strength of evidence as predictive accuracy. The American Statistician, 73, 186–190.

Royall, R. M. (1997). Statistical evidence: A likelihood paradigm. London: Chapman & Hall.

Shalloway, D. (2014). The evidentiary credible region. Bayesian Analysis, 9, 909–922.

Stuart, A., Ord, J. K., & Arnold, S. (1999). Kendall’s advanced theory of statistics vol. 2A: Classical inference & the linear model (6th ed.). London: Arnold.

Verdinelli, I., & Wasserman, L. (1995). Computing Bayes factors using a generalization of the Savage–Dickey density ratio. Journal of the American Statistical Association, 90, 614–618.

Wagenmakers, E.-J., Morey, R. D., & Lee, M. D. (2016). Bayesian benefits for the pragmatic researcher. Current Directions in Psychological Science, 25, 169–176.

Wetzels, R., Grasman, R. P. P. P., & Wagenmakers, E.-J. (2010). An encompassing prior generalization of the Savage–Dickey density ratio test. Computational Statistics & Data Analysis, 54, 2094–2102.

Wrinch, D., & Jeffreys, H. (1921). On certain fundamental principles of scientific inquiry. Philosophical Magazine, 42, 369–390.

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Annalen der Philosophie

Tập 87

589-601

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