Poisson group testing: A probabilistic model for nonadaptive streaming boolean compressed sensing

• Published in: Proceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) pp. 3335 - 3339
• Main Authors: Emad, Amin, Milenkovic, Olgica
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.05.2014
• Subjects: Boolean compressed sensing; Cloning; Compressed sensing; Computational modeling; Dynamical group testing; Information-theoretic bounds; Poisson and Binomial probabilistic group testing; Probabilistic logic; Random variables; Testing; Upper bound
• ISSN: 1520-6149
• DOI: 10.1109/ICASSP.2014.6854218

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model applies to a number of biological testing scenarios, where the subjects are assumed to be ordered based on their arrival times and where the probability of being defective decreases with time. Our main result is an information-theoretic upper bound on the minimum number of tests required to achieve an average probability of detection error asymptotically converging to zero.