Issues in the Bayesian forecasting of dispersal after a nuclear accident
This thesis addresses three main topics related to the practical problems of modelling the spread of nuclear material after an accidental release. The first topic deals with the issue of how qualitative information (expert jUdgement) about the development of the emission of contamination after an accident can be coded as a Dynamic Linear Model (DLM). An illustration is given of the subsequent adaptation of the expert judgement in response to the incoming data. Moreover, the height of the release at the source can be a key parameter in the subsequent dispersal. We addressed uncertainty on the release height using the Multi-Process Models framework. That is we included several models in our analysis, each with a different release height. The Bayesian methodology uses probabilities representing their relative likelihood to weight these and updates the probabilities in the light of monitoring data. A brief illustration of testing the updating algorithm on simulated contamination readings is provided. The second topic concerns the demands of computational efficiency. We show how the Bayesian propagation algorithms on a dynamic junction tree of cliques of variables (representing a high dimensional Gaussian process), as provided by Smith et al. (1995), can be generalised to incorporate the case when data may destroy neat dependencies (i.e. when observations are taken under more than one clique). Here we introduce two classes of new operators: exact and non-exact (approximations) which act on this high dimensional Gaussian process, modifying its junction tree by another tree which allows quicker probability propagation. We also develop fast algorithms which can be defined by approximating Gaussian systems by cutting edges on junctions. The appropriateness ofthe approximations is based on the Kulback-Leibler/Hellinger distances. Some of these new operators and algorithms have been implemented and coded. Preliminary tests on these algorithms were carried out using arbitrary data, and the system proved to be highly efficient in terms of P.C. user time. The third topic concentrates on generalisations from a Gaussian process. It proposes, as a good approximation, an adaptation of the Dynamic Generalised Linear Models (DGLMs) of West, Harrison, and Migon (1985) for updating algorithms on a dynamic junction tree. The Hellinger distance is used to check the accuracy of the dynamic approximation. The analysis of these topics involves a review and extension of some useful theory and results on Bayesian forecasting and dynamic models, graphical modelling, and information divergence.