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Theoretical Entities in Statistical Explanation

Published online by Cambridge University Press:  28 February 2022

James G. Greeno*
Affiliation:
University of Michigan

Extract

The ideas in this paper are based on an analysis of statistical explanation that uses the information transmitted by a theory. Consider a theory that specifies a probability distribution on the events of some domain, where for purposes of analysis we divide the variables that describe the domain into two sets: [M], a set of variables whose values are to be explained, and [S], a set of variables whose values are used to explain the values of the variables in [M]. The information transmitted by the theory is

(1)

where H(S) and H(M) are the uncertainties of the events in [S] and [M], respectively, and H(S x M) is the uncertainty of the joint events.

To illustrate this idea, consider the problem of explaining medical symptoms such as fever, coughing, skin rash and abdominal pain.

Type
Symposium: Theoretical Entities in Statistical Explanation
Copyright
Copyright © Philosophy of Science Association 1970

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References

[1] Bower, G. H., ‘Application of a Model to Paired-Associate Learning’, Psychometrika, 26 (1961) 255-80.CrossRefGoogle Scholar
[2] Greeno, J. G., ‘Evaluation of Statistical Hypotheses Using Information Transmitted’, Philosophy of Science 37 (1970), 279-93.CrossRefGoogle Scholar
[3] Krantz, D. H., ‘Threshold Theories of Signal Detection’, Psychological Review 76 (1969) 308-24.CrossRefGoogle ScholarPubMed
[4] Luce, R. D., ‘A Threshold Theory for Simple Detection Experiments’, Psychological Review 76 (1969) 308-24.Google Scholar