The Limits of the Preponderance of the Evidence Standard: Justifiably Naked Statistical Evidence and Multiple Causation

1982 ◽  
Vol 7 (2) ◽  
pp. 487-516 ◽  
Author(s):  
David Kaye

The preponderance-of-the-evidence standard usually is understood to mean that the plaintiff must show that the probability that the defendant is in fact liable exceeds 1/2. Several commentators and at least one court have suggested that in some situations it may be preferable to make each defendant pay plaintiff's damages discounted by the probability that the defendant in question is in fact liable. This article analyzes these and other decision rules from the standpoint of statistical decision theory. It argues that in most cases involving only one potential defendant, the conventional interpretation of the preponderance standard is appropriate, but it notes an important exception. The article also considers cases involving many defendants, only one of whom could have caused the injury to plaintiff. It argues that ordinarily the single defendant most likely to have been responsible should be liable for all the damages, even when the probability associated with this defendant is less than 1/2. At the same time, it identifies certain multiple-defendant cases in which the rule that weights each defendant's damages by the probability of that defendant's liability should apply.

2002 ◽  
Vol 357 (1420) ◽  
pp. 419-448 ◽  
Author(s):  
Wilson S. Geisler ◽  
Randy L. Diehl

In recent years, there has been much interest in characterizing statistical properties of natural stimuli in order to better understand the design of perceptual systems. A fruitful approach has been to compare the processing of natural stimuli in real perceptual systems with that of ideal observers derived within the framework of Bayesian statistical decision theory. While this form of optimization theory has provided a deeper understanding of the information contained in natural stimuli as well as of the computational principles employed in perceptual systems, it does not directly consider the process of natural selection, which is ultimately responsible for design. Here we propose a formal framework for analysing how the statistics of natural stimuli and the process of natural selection interact to determine the design of perceptual systems. The framework consists of two complementary components. The first is a maximum fitness ideal observer, a standard Bayesian ideal observer with a utility function appropriate for natural selection. The second component is a formal version of natural selection based upon Bayesian statistical decision theory. Maximum fitness ideal observers and Bayesian natural selection are demonstrated in several examples. We suggest that the Bayesian approach is appropriate not only for the study of perceptual systems but also for the study of many other systems in biology.


Author(s):  
Elías Moreno ◽  
Francisco José Vázquez-Polo ◽  
Miguel Ángel Negrín-Hernández

2008 ◽  
Vol 12 (8) ◽  
pp. 291-297 ◽  
Author(s):  
Julia Trommershäuser ◽  
Laurence T. Maloney ◽  
Michael S. Landy

Technometrics ◽  
1998 ◽  
Vol 40 (2) ◽  
pp. 165-165
Author(s):  
S. Panchapakesan ◽  
N. Balakrishnan

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