On the Geometric Interplay Between Goodness-of-Fit and Estimation: Illustrative Examples

摘要: 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 same population parameter compellingly establishes main theme paper: namely, that is necessary but not sufficient for model selection. Visual examples vividly communicate this. Specifically, given estimation problem, we define class least-informative models, linking these to both nonparametric maximum entropy methods. Any other then seen involve an informative rotation, often embodying extra-data considerations. also look at way translation generates form bias-variance trade-off. Overall, our approach global extension pioneering local work by Copas Eguchi which, note, was geometrically inspired.