Exercise 10.5 In ‘chapter 10 dmft scores full data set.odc’ a Poisson-gamma and a negative binomial distribution are fit to the dmft index of the 4352 seven-year-old children of the Signal-Tandmobiel study. In the negative binomial model the logical nodes ‘alpha’ and ‘beta’ are created to show the link with the Poisson-gamma model. Verify this correspondence by making use of formula (3.15) and the WinBUGS Manual. Verify that pD and DIC differ considerably between the negative binomial and the Poisson-gamma model.