Chapter

Evidence Functions and the Optimality of the Law of Likelihood

Subhash R. Lele

in The Nature of Scientific Evidence

Published by University of Chicago Press

Published in print October 2004 | ISBN: 9780226789552
Published online February 2013 | e-ISBN: 9780226789583 | DOI: http://dx.doi.org/10.7208/chicago/9780226789583.003.0007
Evidence Functions and the Optimality of the Law of Likelihood

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This chapter formulates a class of functions, called evidence functions, which may be used to characterize the strength of evidence for one hypothesis over a competing hypothesis. It shows that the strength of evidence is intrinsically a comparative concept, comparing the discrepancies between the data and each of the two hypotheses under consideration. The likelihood ratio, which is commonly suggested as a good measure for the strength of evidence, belongs to this class and corresponds to comparing the Kullback-Leibler discrepancies. The likelihood ratio as a measure of strength of evidence has some important practical limitations: sensitivity to outliers, necessity to specify the complete statistical model, and difficulties in handling nuisance parameters. By using evidence functions based on discrepancy measures such as Hellinger distance or Jeffreys distance, these limitations can be overcome. Provided the model is correctly specified, for a single-parameter case, the likelihood ratio is an optimal measure of the strength of evidence within the class of evidence functions. This result also establishes the connection between the optimality of the estimating functions and the optimality of the evidence functions.

Keywords: evidence functions; evidence; hypotheses; likelihood ratio; Kullback-Leibler discrepancies; Hellinger distance; Jeffreys distance; optimality; outliers; nuisance parameters

Chapter.  10243 words.  Illustrated.

Subjects: Animal Pathology and Diseases

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