Multinomial group testing models with incomplete identification |
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| Institution: | 1. Department of Statistics, University of Haifa, Haifa 31905, Israel;2. Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany;3. Center for Economic Research, Tilburg University, 5000 LE Tilburg, The Netherlands;1. Leibniz Universitaet Hannover, Institute of Biostatistics, Herrenhaeuserstr. 2, 30419, Hannover, Germany;2. University of Canterbury, School of Mathematics & Statistics, Private Bag 4800, Christchurch 8041, New Zealand;1. Institute of Plant Nutrition and Soil Science, Christian Albrechts University Kiel, Hermann-Rodewald Str. 2, D-24118 Kiel, Germany;2. Department of Proteome and Metabolome Research, Faculty of Biology, Bielefeld University, Postfach 100131, D-33501 Bielefeld, Germany;3. Lehrfach Variationsstatistik, Christian Albrechts University Kiel, Hermann-Rodewald Str. 9, D-24118 Kiel, Germany;4. Institute of Crop Science, Quality of Plant Products, University Hohenheim, Schloss, Westhof West, 118, D-70593 Stuttgart, Germany;5. Institute of Applied Plant Nutrition, Plant Nutrition, Georg-August-University Göttingen, Carl-Sprengel-Weg 1, D-37075 Göttingen, Germany;6. Institute of Botany, Technische Universität Dresden, Zellescher Weg 20b, D-01062 Dresden, Germany;1. LGM-ENIM, Faculty of Sciences of Monastir, University of Monastir, Tunisia;2. MAPSFA, National Engineering School of Monastir, University of Monastir, Tunisia;3. Instituto de Estadística, PUCV, Av. Errazuriz 2734, Valparaíso, V región, Chile |
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| Abstract: | We study reliable multinomial probabilistic group testing models with incomplete identification. We assume that every of the pooled items has none or some of k attributes, one of them causing contamination. Any group possessing this latter attribute is discarded, while the others are collected and separated according to the attributes that were found in them. The objective is to choose an optimal group size for pooled screening so as to collect prespecified numbers of items of the various types with minimum testing expenditures. We derive exact results for the underlying distributions of the stopping times, enabling us to find optimal procedures by numerical methods. |
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