A mathematical theory of arguments for statistical evidence
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.
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The Theory of Generalized Functional Models
The Plausibility and Likelihood Functions
Hints on Continuous Frames and Gaussian Linear Systems
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admissible perturbations assumed assumption-based reasoning babies called canonical basis canonical coordinates canonical potential closed hint combined hint commonality function compute conditional distribution consider corresponding covariance matrix define degree of support degrees of plausibility Dempster's rule denote the hint denote the m-function dimes domain equivalent focal sets functional model Furthermore Gaussian hint inferred Gaussian linear system given in equation hint H Hm,o hypothesis H implies incidence matrix Jessica Kalman filter kernel Kohlas & Monney Let H likelihood likelihood function linearly independent mapping marginal Markov tree means Monney 27 observation pl(H plausibility function possible values precise Gaussian hint precise hint pregnant probability density probability density function probability measure Proof R.A. Fisher random perturbation random variable rank(A regular matrix represented set of possible Shafer 44 Shenoy and Shafer shows sp(H subsets support function theorem unknown parameter valuation weight of evidence white balls