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AuthorMonney, Paul-Andrรฉ. author
TitleA Mathematical Theory of Arguments for Statistical Evidence [electronic resource] / by Paul-Andrรฉ Monney
ImprintHeidelberg : Physica-Verlag HD : Imprint: Physica, 2003
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Descript XIII, 154 p. online resource


The subject of this book is the reasoning under uncertainty based on staยญ tistical evidence, where the word reasoning is taken to mean searching for arguments in favor or against particular hypotheses of interest. The kind of reasoning we are using is composed of two aspects. The first one is inspired from classical reasoning in formal logic, where deductions are made from a knowledge base of observed facts and formulas representing the domain speยญ cific knowledge. In this book, the facts are the statistical observations and the general knowledge is represented by an instance of a special kind of staยญ tistical models called functional models. The second aspect deals with the uncertainty under which the formal reasoning takes place. For this aspect, the theory of hints [27] is the appropriate tool. Basically, we assume that some uncertain perturbation takes a specific value and then logically evalยญ uate the consequences of this assumption. The original uncertainty about the perturbation is then transferred to the consequences of the assumption. This kind of reasoning is called assumption-based reasoning. Before going into more details about the content of this book, it might be interesting to look briefly at the roots and origins of assumption-based reasoning in the statistical context. In 1930, R. A. Fisher [17] defined the notion of fiducial distribution as the result of a new form of argument, as opposed to the result of the older Bayesian argument


1. The Theory of Generalized Functional Models -- 2. The Plausibility and Likelihood Functions -- 3. Hints on Continuous Frames and Gaussian Linear Systems -- 4. Assumption-Based Reasoning with Classical Regression Models -- 5. Assumption-Based Reasoning with General Gaussian Linear Systems -- 6. Gaussian Hints as a Valuation System -- 7. Local Propagation of Gaussian Hints -- 8. Application to the Kaiman Filter -- References

Statistics Computer mathematics Statistics Statistics for Business/Economics/Mathematical Finance/Insurance Computational Mathematics and Numerical Analysis


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