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The Curve Fitting Problem: A Bayesian Approach

Published online by Cambridge University Press:  01 April 2022

Prasanta S. Bandyopadhayay ,
Robert J. Boik  and
Susan Vineberg
Prasanta S. Bandyopadhayay
Affiliation:
Montana State University
Robert J. Boik
Affiliation:
Montana State University
Susan Vineberg
Affiliation:
University of Rochester
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Abstract

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes’ theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory’s goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship between simplicity of a theory and its predictive accuracy.

Type
Confirmation
Information
Philosophy of Science , Volume 63 , Issue S3 , 1996 , pp. S264 - S272
Copyright
Copyright © Philosophy of Science Association 1996

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Footnotes

†

Department of Philosophy, Montana State University, Bozeman, MT 59717.

‡

Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717.

§

Simon School of Business and Management, University of Rochester, Rochester, NY 14627.

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