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The Curve Fitting Problem: A Bayesian Rejoinder

Published online by Cambridge University Press:  01 April 2022

Prasanta S. Bandyopadhyay  and
Robert J. Boik
Prasanta S. Bandyopadhyay
Affiliation:
Montana State University
Robert J. Boik*
Affiliation:
Montana State University
*
†Bandyopadhyay: Department of Philosophy, Montana State University, Bozeman, MT 59717; Boik: Department of Mathematical Sciences, Montana State University, Bozeman, MT 59717.
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Abstract

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC.

Type
Probability and Statistical Inference
Information
Philosophy of Science , Volume 66 , Issue S3: Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers Sep., 1999 , 1999 , pp. S390 - S402
Copyright
Copyright © 1999 by the Philosophy of Science Association

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Footnotes

‡

Portions of this paper were presented at the APA, Central Division, 1998. We wish to thank James Allard, Scott DeVito, Malcolm Forster, William Harper, Henry Kyburg, Jr., Eric MacIntyre, Brian Skyrms, Elliot Sober and Greg Wheeler for discussion and encouragement. John G. Bennett and Gordon Brittan, Jr. also deserve special thanks for numerous discussions regarding the content of the paper.

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