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The Curve Fitting Problem: A Bayesian Rejoinder
Published online by Cambridge University Press: 01 April 2022
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
- Copyright
- Copyright © 1999 by the Philosophy of Science Association
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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