Inferring $p$ from the observed number of positives in the sample

Let us finally move to the probabilistic inference of the proportion of infected individuals, $p$, based on the number of positives $n_P$ in a sample of size $n_s$ and given our best knowledge of the performance of the test, all summarized in the graphical model of Fig. ,

Figure: Graphical model of Fig. , re-drawn in order to emphasize its inferential use and including the commands to build up the JAGS model. `$f_0(p)$', left open in this diagram, stands for the prior distribution of $p$.

which differs from that of Fig.  only for the symbol `$\surd$ ' moved from node $p$ (now `unobserved') to node $n_P$ (now `observed'). The diagram contains also the probabilistic and deterministic relations among the nodes, written directly using the JAGS language.⁴⁵