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A Mathematical Theory of Arguments for Statistical Evidence

  • Book
  • © 2003

Overview

Authors:
  1. Paul-André Monney

    1. Department of Statistics, Purdue University, West Lafayette, USA

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Part of the book series: Contributions to Statistics (CONTRIB.STAT.)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XIII
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  2. The Theory of Generalized Functional Models

    • Paul-AndrĂ© Monney
    Pages 1-37

  3. The Plausibility and Likelihood Functions

    • Paul-AndrĂ© Monney
    Pages 39-57

  4. Hints on Continuous Frames and Gaussian Linear Systems

    • Paul-AndrĂ© Monney
    Pages 59-70

  5. Assumption-Based Reasoning with Classical Regression Models

    • Paul-AndrĂ© Monney
    Pages 71-95

  6. Assumption-Based Reasoning with General Gaussian Linear Systems

    • Paul-AndrĂ© Monney
    Pages 97-108

  7. Gaussian Hints as a Valuation System

    • Paul-AndrĂ© Monney
    Pages 109-127

  8. Local Propagation of Gaussian Hints

    • Paul-AndrĂ© Monney
    Pages 129-135

  9. Application to the Kalman Filter

    • Paul-AndrĂ© Monney
    Pages 137-148

  10. Back Matter

    Pages 149-154
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Keywords

About this book

The subject of this book is the reasoning under uncertainty based on sta­ 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 spe­ 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 sta­ 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 eval­ 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.

Reviews

From the reviews:

"The book, clearly written, is structured in two parts comprising two and six chapters, respectively. … The overall quality of the book is very good, the material is well organized and notations and terminology are unified. It is a very good presentation of the state of research in the area of modeling reasoning and an insightful reference for the statistician." (Evdokia Xekalaki, Zentralblatt MATH, Vol. 1100 (2), 2007)

Authors and Affiliations

  • Department of Statistics, Purdue University, West Lafayette, USA

    Paul-André Monney

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