Noisy Pooled PCR for Virus Testing

Junan Zhu; Kristina Rivera; Dror Baron

We now have a linear relationship from x to w, and the noiseless measurements vector w, which contains the number of sick patients per measurement, is then processed by a probabilistic channel to yield the noisy measurements vector, y. Our goal is to estimate x from y, A, and statistical information about the channel. Other group testing approaches often perform pooled measurements in a first part, and positives are tested individually in a second part [3] ; our method can improve both parts by pooling all measurements and accounting for all available information. In the following section, we describe our algorithmic framework in detail. The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.06.026765 doi: bioRxiv preprint Algorithm 1 GAMP Inputs. Maximum iterations t max , percentage of sick patients ρ, false negative probability p 1 , false positive probability p 2 , measurements y, and matrix A. Initialize. t, k, h m , Θ m , x n , s n , ∀m, n. Comment. t is iteration number, k is mean of our estimate for Ax, h m is correction term for w m , Θ m is variance of h, x n is our estimate for x n , s n is variance in our estimate x n . h m = g out (k m , y m , θ m ) 7: