Uncertainty about $\pi_1$ and $\pi_2$

Until now we have used the nominal values of $\pi_1$ and $\pi_2$ of Ref. [16], and have already seen how our probabilistic conclusions change if other sets of values are employed. But these two model parameters come from tests performed on selected people, known with certainty¹⁴ to be infected or not. More precisely $\pi_1=0.98$ results from 400 surely infected, 392 of which resulted positive; $\pi_2=0.12$ from 200 surely not infected, 176 of which resulted negative [16].