Bayesian networks for inference with geographic information systems

This thesis is concerned with Bayesian networks and their applications as inference mechanisms in conjunction with Geographic Information Systems. More specifically the problem that concerns us is the assessment of the risk of desertification of certain burned areas in Attica, Greece by combining data from various sources together with expert knowledge about the desertification process. The first chapters of the thesis are mainly concerned with reviewing the various evidence combining approaches. It is then showed how a Bayesian network is constructed to be used as the inference mechanism with a GIS and how uncertainty in the input data is incorporated in the network. The novelty if this work lies on the development of methodologies to handle both uncertainty in the input data as well as uncertainty in the inference. The latter is achieved by various methodologies which make a contribution to the unexplored area of estimating the parameters, i. e. the conditional probabilities, used by the network to perform reasoning. The first method presented uses an analytic formula which relates the variables of interest. The second methodology developed for estimating the parameters is based on obtaining the correspondence between the Bayesian and neural networks. It is proved that there is a correspondence between the two networks and formulae are derived which relate their parameters, i. e. the weights of the neural network with the conditional probabilities of the Bayesian network. This is of significant importance since the elements of the conditional probability matrix used by the Bayesian network can then be estimated easily given a trained neural network. As a result the Bayesian network will perform the same inference and produce the same results as the corresponding neural network, with the extra advantage that the Bayesian network offers the option of inputing data at any node as well as bidirectional flow of information. All the methodologies outlined above were successfully applied to the Bayesian network constructed for desertification assessment and the results were compared with the classification of experts using field data.