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Fig. 3 | Emerging Themes in Epidemiology

Fig. 3

From: Teaching: confidence, prediction and tolerance intervals in scientific practice: a tutorial on binary variables

Fig. 3

Simulation for Bayesian tolerance intervals. TIs do not need to cover any true parameter, but they contain at least a specified proportion \(P\) of the population with confidence (\(1-\alpha \)). Illustration of the meaning of \((1-\alpha =0.95,P=0.9)\) tolerance intervals based on 100 samples. A single sample is based on \(n=20\) observations generated from a true Be(0.5) distribution, and the TI predicts the number of events in a future sample of size \(m=50\) specifying that at least \(P=0.9\) of the results must be covered by the TI. TIs that have a content less than \(P=0.9\) and do not satisfy the coverage condition \({C}_{x}\left(L,U,\theta \right)\ge 0.9\) (Additional file 1) are coloured red (here, 7 out of 100)

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