
176 PREDICTION OF FUTURE OBSERVATIONS
0.0 0.2 0.4 0.6 0.8 1.0
0.955 0.965 0.975
θ
Coverage
(a) Coverage probability
0.0 0.2 0.4 0.6 0.8 1.0
10 20 30 40 50 60
θ
Average Length
(b) Average length
Figure 9.3 Taken from [179]. Coverage probability and average length of the modified IM
(solid), fiducial (dashed), and Jeffreys prior Bayes (dotted) upper 95% prediction intervals,
as functions of θ; the three curves in panel (b) are indistinguishable. Here n = m = 100 and
estimates are based on 2500 simulated data sets.
ing. However, our examples in Section 9.3 demonstrate that the uniformity assump-
tion of Theorem 9.1 holds at least approximately. Here we give a