Introduction

Drawing together data relevant to different parts of a complex model is a challenge for a number of reasons. First even if the prior density has a simple and interpretable form before any sampling has taken place, sampling may well introduce dependences across large sections of the model. If this happens then the salient features needed for inference can become much more difficult to calculate and this can be critical. Even more of a problem is when the values of certain variables remain unsampled.

However sometimes this is not the case. It is not unusual for the DM to be able to assume that different functions of the data sets she has at hand inform only certain factors in the credence decomposition she chooses. However the circumstances when such assumptions are transparent – or failing that plausible – are closely linked to how sampling schemes, observational studies and experiments are designed. In the last chapter we focused on decision models that could be structured round a BN. We showed how the decomposition of a problem into smaller explanatory components not only made a dependence structure more explicit but also provided a framework for the fast propagation of evidence using local structure in the large joint probability space. Now hierarchical models have been a bedrock of Bayesian modelling for some time and these are usually expressible as a BN.