Applied Bayesian Modelling - Free

ENSEMBLE ESTIMATES: POOLING OVER SIMILAR UNITS 57With an arbitrary value of k ˆ 10, a three chain run (Model A in Program 2.6) showsearly convergence and summaries are based on the last 24 500 iterations from 25 000.This leads to a posterior mean value for f 2 of 62.5, and to smoothed program effects m jranging from 5.3 to 11.7, as represented in terms of posterior means (see Table 2.8).Then (Model B) uncertainty in k is introduced via an exponential prior,k E(0:01)Table 2.8Program effects: observed and smoothedSchool Effectiveness DataSchool Y s s 2 1=s 2A 28.39 14.9 222 0.0045B 7.94 10.2 104 0.0096C 2.75 16.3 265.7 0.0038D 6.82 11 121 0.0083E 0.64 9.4 88.4 0.0113F 0.63 11.4 130 0.0077G 18.01 10.4 108.2 0.0092H 12.16 17.6 309.8 0.0032Sum of 1=s 2 0.0576Harmonic Mean 138.81 ˆ (8/0.0576)for VarianceSmoothed Effects Model AModel BMean 2.5% 97.5% Mean 2.5% 97.5%m 1 11.7 5.3 34.8 m 1 11.4 4.8 34.8m 2 8.0 7.7 23.8 m 2 8.0 7.5 23.5m 3 6.4 14.6 24.4 m 3 6.5 14.2 24.0m 4 7.7 8.4 23.8 m 4 7.7 8.5 23.5m 5 5.3 11.4 19.5 m 5 5.5 11.3 19.5m 6 6.2 11.5 21.8 m 6 6.3 11.8 21.8m 7 11.0 3.9 29.3 m 7 10.6 3.9 28.9m 8 8.7 10.4 29.1 m 8 8.5 10.3 29.0f 2 62.6 4.3 412.9 f 2 58.5 0.9 423.0M 8.1 3.7 20.2 M 8.1 3.8 20.3k 47.3 0.2 304.8Model CMean 2.50% 97.50%m 1 10.19 1.11 26.00m 2 8.15 2.73 19.68m 3 7.20 6.90 19.65m 4 8.05 3.44 19.85m 5 6.61 5.88 17.48m 6 7.20 5.11 18.74m 7 9.72 0.64 22.44m 8 8.60 4.06 22.52f 2 4.23 0.06 14.15