Introduction

The last chapter showed how decision problems with many different simultaneous objectives can be addressed using the formal techniques developed earlier in this book. We now turn to a related problem where – as in the last example of that chapter – the processes describing the DM's beliefs is high dimensional. Formally of course this presents no great extension from those described in the early part of this book. The theory leading to expected utility maximising strategies applies just as much to problems where uncertainty is captured through distributions of high-dimensional vectors of random variables as to much simpler ones.

However from the practical point of view a Bayesian decision analysis in this more complicated setting is by no means so straightforward to enact. A joint probability space requires an enormous number of joint prior probabilities to be elicited, often from different domain experts. For the analyst to resource the DM to build a framework that on the one hand faithfully and logically combines the informed descriptions of diverse features of the problem and on the other supports both the calculation of optimal policies and diagnostics to check the continuing veracity of the system presents a significant challenge.

With the increase in electronic data collection and storage many authors have recognised this challenge and developed ways of securely building faithful Bayesian models even when the processes are extremely large.