Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T23:39:18.916Z Has data issue: false hasContentIssue false
  • English
  • Français

The characterisation of scoring functions

Part of: Foundations of probability theory

Published online by Cambridge University Press:  09 April 2009

Michael A. B. Deakin
Michael A. B. Deakin
Affiliation:
Department of Mathematics and Statistics Monash University Clayton Vic3168Australia e-mail:[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The literature on subjective probabilities contains a number of functions that have been proposed as ‘scoring functions’. The principal requirement is that, with several events that may occur in the future and to which subjective ‘probabilities’ are assigned, the expected score given by these ‘probabilities’ will be extremised if the values assigned equal the ‘true probabilities’ of the various outcomes. This article discusses the question of what other scoring functions might be used (beyond those so far proposed).

MSC classification

Secondary: 60A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 1 , August 2001 , pp. 135 - 147
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Chrystal, G., Algebra: an elementary textbook, 7th edition (Chelsea, New York, 1964).Google Scholar
[2]Deakin, M. A. B., ‘Scoring functions for football-tipping and other such contests’, Gaz. Aust. Math. Soc. 26(1999), 15–18.Google Scholar
[3]de Finetti, B., Theory of probability, Vol. 1 (Wiley, London, 1974), Ch. 5.Google Scholar
[4]Rektorys, K. et al. , Survey of applicable mathematics, English edition (Iliffe, London, 1969).Google Scholar
[5]Savage, L. J., ‘Elicitation of personal probabilities and expectations’, J. Amer. Statist. Assoc. 66 (1971), 783–801.Google Scholar
[6]Schervish, M. J., ‘A general method for comparing probability assessors’, Ann. Statist. 17 (1989), 1856–1879.Google Scholar
[7]Winkler, R. L., ‘Scoring rules and the evaluation of probability assessors’, J. Amer Statist. Assoc. 64(1969), 1073–1078.Google Scholar
[8]Winkler, R. L., ‘Judgments under uncertainty’, in: Encyclopaedia Statist. Sci., (‘Kotz-Johnson’) Vol. 4 (Wiley, New York, 1983) pp. 332–336.Google Scholar
[9]Winkler, R. L., ‘Scoring rules and the evaluation of probabilities’, Test 5 (1996), 1–60.Google Scholar