Contributions to Statistics

A Mathematical Theory of Arguments for Statistical Evidence

Authors: Monney, Paul-Andre

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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)


Table of contents (8 chapters)

  • The Theory of Generalized Functional Models

    Monney, Paul-André

    Pages 1-37

  • The Plausibility and Likelihood Functions

    Monney, Paul-André

    Pages 39-57

  • Hints on Continuous Frames and Gaussian Linear Systems

    Monney, Paul-André

    Pages 59-70

  • Assumption-Based Reasoning with Classical Regression Models

    Monney, Paul-André

    Pages 71-95

  • Assumption-Based Reasoning with General Gaussian Linear Systems

    Monney, Paul-André

    Pages 97-108

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-3-642-51746-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-7908-1527-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Mathematical Theory of Arguments for Statistical Evidence
Authors
Series Title
Contributions to Statistics
Copyright
2003
Publisher
Physica-Verlag Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-51746-4
DOI
10.1007/978-3-642-51746-4
Softcover ISBN
978-3-7908-1527-6
Series ISSN
1431-1968
Edition Number
1
Number of Pages
XIII, 154
Topics