A Mathematical Theory of Arguments for Statistical Evidence

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The subject of this book is the reasoning under uncertainty based on statistical evidence. The concepts are developed, explained and illustrated in the context of the mathematical theory of hints, which is a variant of the Dempster-Shafer theory of evidence. In the first two chapters, the theory of generalized functional models for a discrete parameter is developed, which leads to a general notion of weight of evidence. The second part of the book is dedicated to the study of special linear functional models called Gaussian linear systems. Finally, it is shown that the celebrated Kalman filter can easily be derived by local propagation of Gaussian hints in a Markov tree.