Fig. 5.
Item limits in sampling models. For each model, A, C, E, and G show how the probability distribution of the number of items recovered with greater than zero precision (A and C; greater than a fixed threshold for E and G) changes with set size (color coded, increasing blue to red; discrete probability distributions are depicted as line plots for better visualization). B, D, F, and H plot the mean number of items with above-threshold precision as a function of set size for different threshold values. Thresholds are defined as a proportion of the base precision . (A and B) In the fixed sampling model, the number of items with nonzero precision increases with set size, then plateaus when the number of items equals the number of samples. (C and D) The stochastic sampling model with Poisson variability also has a limit on the number of items with nonzero precision, although this limit is probabilistic and emerges asymptotically (converging to the distribution shown by the red curve in C for large set sizes, corresponding to the mean number of items plotted as black curve in D). (E and F) Stochastic models with lower discretization display similar probabilistic item limits for precision exceeding a fixed threshold, but with the expected number of items saturating at different values depending on threshold (different colors in F). (G and H) This property also extends to models with continuous precision distributions.