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Bayes-optimal estimation of overlap between populations of fixed size

Fig 2

Inference and uncertainty using the posterior.

The posterior distribution over s is plotted for the realistic scenario of n_a = 47, n_b = 32, and n_ab = 20 [line; Eq (6)]. The posterior mean provides our estimate of the true overlap [open circle; Eq (7)], and the interval accounting for at least 90% of the area under the posterior curve provides an equal-tailed 90% credible interval [shading; Eq (8)]. The estimate is shown for comparison [black cross; Eq (1)], and is typically less than or equal to .

doi: https://doi.org/10.1371/journal.pcbi.1006898.g002