16. Consider again the stack loss data originally presented in Example 2.16.

Suppose we wish to compare the assumptions of normal, t4, and DE errors for these data.

(a) Repeat the outlier analysis in Example 4.7 for these data. Do the λi posteriors for the nonnormal models effectively identify the outliers?

(b) Use the Comparison tool to obtain a side-by-side comparison of the boxplots of the posterior median θ across the three error models, similar to Figure 4.9. Then do a similar comparison of the width of the central 95% credible interval for the errors, q.975(σ) − q.025(σ), and explain any differences. (Hint: Dump the σ(g) Gibbs samples into R using the Coda function in WinBUGS, convert them to the quantile difference scale, and then do the boxplot comparison. Use the qnorm and qt functions in R; the DE quantiles can be determined analytically.)

(c) Repeat the DIC analysis in Example 4.8 for these data. What model is DIC-best? Are negative pD values again a problem here?