Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-23T00:32:25.346Z Has data issue: false hasContentIssue false
  • English
  • Français

Hypothesis Testing, “Dutch Book” Arguments, and Risk

Published online by Cambridge University Press:  01 January 2022

Daniel Malinsky
Get access Rights & Permissions [Opens in a new window]

Abstract

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices (like fixed-level null hypothesis significance testing), partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually endorsed by practicing experimentalists.

Type
Confirmation Theory
Information
Philosophy of Science , Volume 82 , Issue 5 , December 2015 , pp. 917 - 929
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I would like to thank Liam Kofi Bright, David Danks, Greg Gandenberger, Clark Glymour, and Teddy Seidenfeld for enlightening discussions on the topic of this article and comments on earlier drafts.

References

ATLAS Collaboration. 2012. “Observation of a New Particle in the Search for the Standard Model Higgs Boson with the ATLAS Detector at the LHC.” Physics Letters B 716 (1): 1–29.CrossRefGoogle Scholar
Berry, Scott, and Viele, Kert. 2008. “A Note on Hypothesis Testing with Random Sample Sizes and Its Relationship with Bayes Factors.” Journal of Data Science 6:75–87.CrossRefGoogle Scholar
Christensen, David. 1996. “Dutch-Book Arguments Depragmatized: Epistemic Consistency for Partial Believers.” Journal of Philosophy 93 (9): 450–79.CrossRefGoogle Scholar
Collaboration, CMS. 2012. “Observation of a New Boson at a Mass of 125 GeV with the CMS Experiment at the LHC.” Physics Letters B 716 (1): 30–61.Google Scholar
Cox, David R. 1958. “Some Problems Connected with Statistical Inference.” Annals of Mathematical Statistics 29:357–63.CrossRefGoogle Scholar
de Finetti, Bruno. 1937/1937. Foresight: Its Logical Laws, Its Subjective Sources. Trans. Kyburg, H. E. Jr. In Studies in Subjective Probability, ed. Kyburg, H. E. Jr. and Smokier, H. E., 93–158. New York: Wiley.Google Scholar
Franklin, Allan. 2013. Shifting Standards: Experiments in Particle Physics in the 20th Century. Pittsburgh: University of Pittsburgh Press.CrossRefGoogle Scholar
Glymour, Clark. 1980. Theory and Evidence. Princeton, NJ: Princeton University Press.Google Scholar
Hájek, Allan. 2005. “Scotching Dutch Books?” Philosophical Perspectives 19:139–51.CrossRefGoogle Scholar
Helland, Inge S. 1995. “Simple Counterexamples against the Conditionality Principle.” American Statistician 49 (4): 351–56.Google Scholar
James, Frederick. 2006. Statistical Methods in Experimental Physics. 2nd ed. Hackensack, NJ: World Scientific.CrossRefGoogle Scholar
Kyburg, Henry. 1978. “Subjective Probability: Criticisms, Reflections, and Problems.” Journal of Philosophical Logic 7 (1): 157–80.CrossRefGoogle Scholar
Lehmann, Erich, and Romano, Joseph P.. 2005. Testing Statistical Hypotheses. 3rd ed. New York: Springer.Google Scholar
Ramsey, Frank P. 1926/1926. “Truth and Probability.” In Foundations of Mathematics and Other Logical Essays, ed. Braithwaite, R. B., 156–98. London: Routledge & Kegan Paul.Google Scholar
Schervish, Mark J., Seidenfeld, Teddy, and Kadane, Joseph B.. 2002. “A Rate of Incoherence Applied to Fixed-Level Testing.” Philosophy of Science 69 (Proceedings): S248–S264.CrossRefGoogle Scholar
Seidenfeld, Teddy, and Kadane, Joseph B. 2009. “Proper Scoring Rules, Dominated Forecasts, and Coherence.” Decision Analysis 6 (4): 202–21.Google Scholar
Seidenfeld, Teddy, Schervish, Mark J., and Kadane, Joseph B.. 1990. “Decisions without Ordering.” In Acting and Reflecting, ed. Sieg, W., 143–70. Dordrecht: Kluwer.Google Scholar