Statistical decision rules concerning synteny or independence between markers

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.

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Expanded Statistical Decision Rules for Interpretations of Results of Rodent Carcinogenicity Studies of Pharmaceuticals

Biopharmaceutical Applied Statistics Symposium - ICSA Book Series in Statistics ◽

10.1007/978-981-10-7820-0_8 ◽

2018 ◽

pp. 151-183

Author(s):

Karl K. Lin ◽

Mohammad A. Rahman

Keyword(s):

Decision Rules ◽

Statistical Decision ◽

Rodent Carcinogenicity

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A Novel Intelligent Technique of Invariant Statistical Embedding and Averaging via Pivotal Quantities for Optimization or Improvement of Statistical Decision Rules under Parametric Uncertainty

WSEAS TRANSACTIONS ON MATHEMATICS ◽

10.37394/23206.2020.19.3 ◽

2020 ◽

Vol 19 ◽

Keyword(s):

Probability Distributions ◽

Decision Rules ◽

Parametric Uncertainty ◽

Decision Criterion ◽

Unknown Parameters ◽

Statistical Decision ◽

Intelligent Technique ◽

Statistical Decisions ◽

Statistical Tolerance ◽

Future Outcomes

In the present paper, for intelligent constructing efficient (optimal, uniformly non-dominated, unbiased, improved) statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a decision criterion and averaging this criterion over pivots’ probability distributions is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, the technique of invariant statistical embedding and averaging via pivotal quantities (ISE&APQ) is independent of the choice of priors and represents a novelty in the theory of statistical decisions. It allows one to eliminate unknown parameters from the problem and to find the efficient statistical decision rules, which often have smaller risk than any of the well-known decision rules. The aim of the present paper is to show how the technique of ISE&APQ may be employed in the particular case of optimization, estimation, or improvement of statistical decisions under parametric uncertainty. To illustrate the proposed technique of ISE&APQ, illustrative examples of intelligent constructing exact statistical tolerance limits for prediction of future outcomes coming from log-location-scale distributions under parametric uncertainty are given

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