Hostname: page-component-84b7d79bbc-5lx2p Total loading time: 0 Render date: 2024-07-28T22:43:31.568Z Has data issue: false hasContentIssue false
  • English
  • Français

Focused Correlation, Confirmation, and the Jigsaw Puzzle of Variable Evidence

Published online by Cambridge University Press:  01 January 2022

Maximilian Schlosshauer  and
Gregory Wheeler
Get access Rights & Permissions [Opens in a new window]

Abstract

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. Wheeler and Scheines have shown that a difference in incremental confirmation of two evidence sets is robustly tracked by a difference in their focus correlation. In this essay, we generalize that tracking result by allowing for evidence having unequal relevance to the hypothesis. Our result is robust as well, and we retain conditions for bidirectional tracking between incremental confirmation measures and focused correlation.

Type
Research Article
Information
Philosophy of Science , Volume 78 , Issue 3 , July 2011 , pp. 376 - 392
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

‡

This work was supported by the European Science Foundation, the Portuguese Science and Technology Foundation, and the Danish Natural Science Research Council.

References

Bovens, L. and Hartmann, S.. 2003. Bayesian Epistemology. Oxford: Oxford University Press.Google Scholar
Bovens, L. and Hartmann, S.. 2006. “An Impossibility Result for Coherence Rankings.” Philosophical Studies 128:77–91.CrossRefGoogle Scholar
Carnap, R. 1962. The Logical Foundations of Probability. 2nd ed. Chicago: University of Chicago Press.Google Scholar
Christensen, D. 1999. “Measuring Confirmation.” Journal of Philosophy 96:437–61.CrossRefGoogle Scholar
Cohen, L. J. 1977. The Probable and the Provable. Oxford: Clarendon.CrossRefGoogle Scholar
Crupi, V., Tentori, K., and Gonzalez, M.. 2007. “On Bayesian Measures of Evidential Support: Theoretical and Empirical Issues.” Philosophy of Science 74 (2): 229–52.CrossRefGoogle Scholar
Danks, D., and Glymour, C.. 2001. “Linearity Properties of Bayes Nets with Binary Variables.” In Uncertainty in Artificial Intelligence: Proceedings of the 17th Conference, ed. Breese, J. and Koller, D., 88–104. San Francisco: Kaufmann.Google Scholar
Eells, E., and Fitelson, B.. 2002. “Symmetries and Asymmetries in Evidential Support.” Philosophical Studies 107 (2): 129–42.CrossRefGoogle Scholar
Joyce, J. 1999. The Foundations of Causal Decision Theory. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Kemeny, J., and Oppenheim, P.. 1952. “Degrees of Factual Support.” Philosophy of Science 19:307–24.CrossRefGoogle Scholar
Keynes, J. M. 1921. A Treatise on Probability. London: Macmillan.Google Scholar
Kyburg, H. E. Jr. 1983. “Recent Work in Inductive Logic.” In Recent Work in Philosophy, ed. Machan, T. and Lucey, K., 87–150. Totowa, NJ: Rowman & Allanheld.Google Scholar
Milne, P. 1997. “Is the One True Measure of Confirmation.” Philosophy of Science 63:21–26.CrossRefGoogle Scholar
Myrvold, W. 1996. “Bayesianism and Diverse Evidence: A Reply to Andrew Wayne.” Philosophy of Science 63:661–65.CrossRefGoogle Scholar
Myrvold, W.. 2003. “A Bayesian Account of the Virtue of Unification.” Philosophy of Science 70:399–423.CrossRefGoogle Scholar
Olsson, E. 2005. Against Coherence: Truth, Probability and Justification. Oxford: Oxford University Press.CrossRefGoogle Scholar
Silva, R., Glymour, C., Scheines, R., and Spirtes, P.. 2006. “Learning the Structure of Latent Linear Structure Models.” Journal of Machine Learning Research 7:191–246.Google Scholar
Wheeler, G. 2009. “Focused Correlation and Confirmation.” British Journal for the Philosophy of Science 60 (1): 79–100.CrossRefGoogle Scholar
Wheeler, G., and Scheines, R.. 2011. “Causation, Association, and Confirmation.” In Explanation, Prediction, and Confirmation: New Trends and Old Ones Reconsidered. The Philosophy of Science in a European Perspective. Dordrecht: Springer.Google Scholar