Curve Fitting, the Reliability of Inductive Inference, and the Error-Statistical Approach.
The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the 'fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on...
| Published in: | Philosophy of Science Vol. 74; no. 5; pp. 1046 - 1067 |
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| Format: | Article |
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Cambridge University Press
Dec2007
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| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=32869881&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 32869881 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00318248 PSC jtl: Philosophy of Science issn: 00318248 maglogo: N pubinfo: dt: Dec2007 vid: 74 iid: 5 pid: 15979 pub: Cambridge University Press artinfo: ui: 32869881 10.1086/525643 ppf: 1046 ppct: 21 formats: fmt: @attributes: type: P size: 373KB tig: atl: Curve Fitting, the Reliability of Inductive Inference, and the Error-Statistical Approach. aug: au: Spanos, Aris affil: Department of Economics, Virginia Tech 3019 Pamplin Hall (0316), Blacksburg, VA 24061 su: Curve fitting Graphic methods in statistics Statistical correlation Numerical analysis Smoothing (Numerical analysis) sug: subj: Curve fitting Graphic methods in statistics Statistical correlation Numerical analysis Smoothing (Numerical analysis) ab: The main aim of this paper is to revisit the curve fitting problem using the reliability of inductive inference as a primary criterion for the 'fittest' curve. Viewed from this perspective, it is argued that a crucial concern with the current framework for addressing the curve fitting problem is, on the one hand, the undue influence of the mathematical approximation perspective, and on the other, the insufficient attention paid to the statistical modeling aspects of the problem. Using goodness-of-fit as the primary criterion for 'best', the mathematical approximation perspective undermines the reliability of inference objective by giving rise to selection rules which pay insufficient attention to 'accounting for the regularities in the data'. A more appropriate framework is offered by the error-statistical approach, where (i) statistical adequacy provides the criterion for assessing when a curve captures the regularities in the data adequately, and (ii) the relevant error probabilities can be used to assess the reliability of inductive inference. Broadly speaking, the fittest curve (statistically adequate) is not determined by the smallness if its residuals, tempered by simplicity or other pragmatic criteria, but by the nonsystematic (e.g. white noise) nature of its residuals. The advocated error-statistical arguments are illustrated by comparing the Kepler and Ptolemaic models on empirical grounds. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Philosophy of Science is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Philosophy of Science holder: Cambridge University Press dt: @attributes: year: 2007 holdings: @attributes: islocal: N |
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