We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the log-likelihood under each model, from which we derive measures of fit and complexity (the effective number of parameters). These may be combined into a Deviance Information Criterion (DIC), which is shown to have an approximate decision-theoretic justification. Analytic and asymptotic identities reveal the measure of complexity to be a generalisation of a wide range of previous suggestions, with particular reference to the neural network literature. The contributions of individual observations to fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. The procedure is illustrated in a number of examples, and throughout it is emphasised that the required quantities are trivial to compute in a Markov chain Monte Carlo analysis, and require no analytic work for new...

Our objectives in this report are to argue the importance of developing a single, consistent mechanism for handling uncertainty throughout RODOS and to demonstrate that Bayesian approaches to decision support with their coherent use of probability to represent uncertainty provide such a mechanism. We emphsise that uncertainty handling includes a number of important issues from data assimilation and the inclusion of expert judgement through to communicating realistic assessments of uncertainty to the decision makers. We also emphasise that the uncertainty handling mechanism must integrate seamlessly with the evaluation modules within RODOS. RODOS is to be a decision support system built upon a client server architecture...

Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling