On the geometric interplay between goodness-of-fit and estimation: Illustrative examples

Karim Anaya-Izquierdo, Paul Marriott, Paul Vos, Frank Critchley

Research output: Chapter in Book/Report/Conference proceedingChapter

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.
Original languageEnglish
Title of host publicationComputational Information Geometry
Subtitle of host publicationFor Image and Signal Processing
EditorsFrank Nielsen, Kit Dodson, Frank Critchley
PublisherSpringer
Pages63-77
ISBN (Electronic)9783319470580
ISBN (Print)9783319470566
Publication statusPublished - 2017

Publication series

NameSignals and Communication Technology

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Anaya-Izquierdo, K., Marriott, P., Vos, P., & Critchley, F. (2017). On the geometric interplay between goodness-of-fit and estimation: Illustrative examples. In F. Nielsen, K. Dodson, & F. Critchley (Eds.), Computational Information Geometry : For Image and Signal Processing (pp. 63-77). (Signals and Communication Technology). Springer.