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The Nature of Scientific EvidenceStatistical, Philosophical, and Empirical Considerations$
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Mark L. Taper and Subhash R. Lele

Print publication date: 2004

Print ISBN-13: 9780226789552

Published to Chicago Scholarship Online: February 2013

DOI: 10.7208/chicago/9780226789583.001.0001

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Statistical Distances as Loss Functions in Assessing Model Adequacy

Statistical Distances as Loss Functions in Assessing Model Adequacy

Chapter:
(p.439) 14 Statistical Distances as Loss Functions in Assessing Model Adequacy
Source:
The Nature of Scientific Evidence
Author(s):

Bruce G. Lindsay

Publisher:
University of Chicago Press
DOI:10.7208/chicago/9780226789583.003.0014

This chapter takes on the problem of model adequacy and makes an argument for reformulating the way model-based statistical inference is carried out. In the new formulation, it does not treat the model as “truth.” It is instead an approximation to truth. Rather than testing for model fit, an integral part of the proposed statistical analysis is to assess the degree to which the model provides adequate answers to the statistical questions being posed. One method for doing so is to create a single overall measure of inadequacy that evaluates the degree of departure between the model and truth. The chapter argues that there are two components of errors in any statistical analysis. One component is due to model misspecification; that is, the working model is different from the true data-generating process. The chapter compares confidence intervals on model misspecification error with external knowledge of the scientific relevance of prediction variability to address the issue of scientific significance. The chapter also analyzes several familiar measures of statistical distances in terms of their possible use as inadequacy measures.

Keywords:   model adequacy, statistical inference, errors, statistical analysis, model misspecification, confidence intervals, scientific significance, prediction variability, statistical distances

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