Fig. 4.

Illustration of the hierarchical model from Box 1 with parameters $\psi =0.3$, ${ϵ}_{01}=0.1$ and ${ϵ}_{10}=0.7$ (dashed vertical lines). A: expected distributions of the number of reported detections at occupied (filled, orange) and not occupied locations (open, black) for $m=5$ visits per location. B and C: Posterior distributions on $\psi$ (B), ${ϵ}_{01}$ (C, black) and ${ϵ}_{10}$ (C, orange) for data simulated at $L={10}^4$ (solid), $L={10}^3$ (dashed) and $L={10}^2$ (dotted) locations with $m=5$ visits each. D: Accuracy of inferring $\psi$ as quantified by the root mean squared deviation (RMSD) of the posterior means of $\psi$ across 100 replicate simulations for different combinations of locations L and visits $m$ for $Lm={10}^5$ (solid) and $Lm={10}^4$ (dashed) total number of visits