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In this paper we define for a Bernoulli samples the \emph{ empirical infection measure}, which counts the number of positives (infections) in the Bernoulli sample and for the \emph{ pool samples} we define the empirical pool infection measure, which counts the number of positive (infected) pool samples. For this empirical measures we prove a joint large deviation principle for Bernoulli samples. We also found an asymptotic relationship between the \emph{ proportion of infected individuals } with respect to the samples size, $n$ and the \emph{ proportion of infected pool samples} with respect to the number of pool samples, $k(n).$ All rate functions are expressed in terms of relative entropies.

Author

Doku-Amponsah, Kwabena

Published

2020

Language

EN