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Anaya-Izquierdo, Karim; Critchley, Frank; Marriott, Paul and Vos, Paul
(2016).
DOI: https://doi.org/10.1007/978-3-319-47058-0_3
Abstract
We show how information geometry throws new light on the interplay between goodness-of-fit and estimation, a fundamental issue in statistical inference. A geometric analysis of simple, yet representative, models involving the same population parameter compellingly establishes the main theme of the paper: namely, that goodness-of-fit is necessary but not sufficient for model selection. Visual examples vividly communicate this. Specifically, for a given estimation problem, we define a class of least-informative models, linking these to both nonparametric and maximum entropy methods. Any other model is then seen to involve an informative rotation, often embodying extra-data considerations. We also look at the way that translation of models generates a form of bias-variance trade-off. Overall, our approach is a global extension of pioneering local work by Copas and Eguchi which, we note, was also geometrically inspired.
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About
- Item ORO ID
- 47975
- Item Type
- Book Section
- ISBN
- 3-319-47056-6, 978-3-319-47056-6
- ISSN
- 1860-4862
- Project Funding Details
-
Funded Project Name Project ID Funding Body Emerging Geometries for Statistical Science: Articulating the Vision. (XM-12-086-FC) EP/L010429/1 EPSRC (Engineering and Physical Sciences Research Council) - Keywords
- signal, image and speech processing; statistics and computing; statistics programs; probability theory; stochastic processes; coding theory; information theory; biomedical engineering
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2017 Springer
- Depositing User
- Radka Sabolova