ABSTRACT
So far, we have relied primarily upon the normal, binomial, and Poisson distributions, and hierarchical combinations of these, for modeling data and parameters. The use of a limited class of distributions results, however, in a limited and potentially inappropriate class of inferences. Many problems fall outside the range of convenient models, and models should be chosen to fit the underlying science and data, not simply for their analytical or computational convenience. As illustrated in Chapter 5, often the most useful approach for creating realistic models is to work hierarchically, combining simple univariate models. If, for convenience, we use simplistic models, it is important to answer the following question: in what ways does the posterior inference depend on extreme data points and on unassessable model assumptions? We have already discussed, in Chapter 6, the latter part of this question, which is essentially the subject of sensitivity analysis; here we return to the topic in greater detail, using more advanced computational methods.
