Probabilistic existence theorems in group testing

For a wide range of combinatorial group testing problems including additive, binary and multiaccess channel models, a probabilistic method is developed to derive upper bounds for the length of optimal nonsequential designs. A general result is proven allowing in many particular cases to compute the...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2003-07, Vol.115 (1), p.1-43
Main Author: Zhigljavsky, Anatoly
Format: Article
Language:English
Subjects:
Applied sciences
Decision theory
Exact sciences and technology
Existence theorems
Experimental design
Factor screening
Group testing
Mathematical analysis
Mathematical programming
Mathematics
Measure and integration
Multiaccess channel
Operational research and scientific management
Operational research. Management science
Optimum experimental design
Probabilistic method
Probability and statistics
Sciences and techniques of general use
Searching with lies
Significant factors
Statistics
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Summary:For a wide range of combinatorial group testing problems including additive, binary and multiaccess channel models, a probabilistic method is developed to derive upper bounds for the length of optimal nonsequential designs. A general result is proven allowing in many particular cases to compute the asymptotic bounds. The existence theorems are also derived for the situation when several errors in the test results can occur (searching with lies) and for the group testing problem in the binomial sample.
ISSN:0378-3758
1873-1171
DOI:10.1016/S0378-3758(02)00148-9