ABSTRACT
All models used to analyze data rely on assumptions to varying degrees. In the Bayesian approach to statistics these modeling assumptions are based on prior beliefs, although in practice, like in classical statistics, they are often informally updated in light of seeing the data; see the discussion in Chapter 8 on the dangers of over-˜tting and under-representing uncertainty due to a reliance on a single chosen model following data-driven model selection. Clearly when the data come from designed experiments, the same prior beliefs should inform both the experimental design and the model with which the data will be analyzed. In these cases, it typically leads to the same models being applied as would be by classical statisticians, even though the theoretical justi˜cation can be quite different. Given that it is unlikely that we can be totally certain about all aspects of a model, it is important that we assess the sensitivity of the inferences to the assumptions made. The most obvious way to do this is to reanalyze the data with a range of different models re¯ecting alternative credible assumptions. In this chapter, we discuss some features of BugsXLA that allow models to be speci˜ed that are inherently more robust to certain types of assumptions.
