The Curve Fitting Problem: A Bayesian Rejoinder
- 1 January 1999
- journal article
- Published by Cambridge University Press (CUP) in Philosophy of Science
- Vol. 66 (S3) , S390-S402
- https://doi.org/10.1086/392740
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.Keywords
This publication has 11 references indexed in Scilit:
- Akaike Information Criterion, Curve-fitting, and the Philosophical Problem of SimplicityThe British Journal for the Philosophy of Science, 1997
- Prediction with vague prior knowledgeCommunications in Statistics - Theory and Methods, 1996
- The Curve Fitting Problem: A Bayesian ApproachPhilosophy of Science, 1996
- How to Tell When Simpler, More Unified, or LessAd HocTheories will Provide More Accurate PredictionsThe British Journal for the Philosophy of Science, 1994
- Descriptive and Inductive SimplicityPublished by JSTOR ,1994
- Statistical Decision Theory and Bayesian AnalysisPublished by Springer Nature ,1985
- A Bayesian analysis of the minimum AIC procedureAnnals of the Institute of Statistical Mathematics, 1978
- Information Criteria for Discriminating Among Alternative Regression ModelsEconometrica, 1978
- Estimating the Dimension of a ModelThe Annals of Statistics, 1978
- Goodness of prediction fitBiometrika, 1975