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Asymptotics of pooling design performance

Part of: Combinatorics

Published online by Cambridge University Press:  14 July 2016

J. K. Percus ,
O. E. Percus ,
W. J. Bruno  and
D. C. Torney
J. K. Percus*
Affiliation:
New York University
O. E. Percus*
Affiliation:
New York University
W. J. Bruno*
Affiliation:
Los Alamos National Laboratory
D. C. Torney*
Affiliation:
Los Alamos National Laboratory
*
∗Postal address: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10021, USA.
∗Postal address: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10021, USA.
∗∗∗Postal address: Theoretical Biology and Biophysics, Los Alamos National Laboratory, T-1O, MS K710, Los Alamos, New Mexico 87545, USA.
∗∗∗Postal address: Theoretical Biology and Biophysics, Los Alamos National Laboratory, T-1O, MS K710, Los Alamos, New Mexico 87545, USA.
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Abstract

We analyse the expected performance of various group testing, or pooling, designs. The context is that of identifying characterized clones in a large collection of clones. Here we choose as performance criterion the expected number of unresolved ‘negative’ clones, and we aim to minimize this quantity. Technically, long inclusion–exclusion summations are encountered which, aside from being computationally demanding, give little inkling of the qualitative effect of parametric control on the pooling strategy. We show that readily-interpreted re-summation can be performed, leading to asymptotic forms and systematic corrections. We apply our results to randomized designs, illustrating how they might be implemented for approximating combinatorial formulae.

Keywords

Approximation techniquesasymptotic analysiscombinatorial designsdiscrete probability

MSC classification

Secondary: 05A: Enumerative combinatorics
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 4 , December 1999 , pp. 951 - 964
Copyright
Copyright © Applied Probability Trust 1999 

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