# A Mathematical Theory of Arguments for Statistical Evidence

• Paul-André Monney
Book

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

1. Front Matter
Pages I-XIII
2. Paul-André Monney
Pages 1-37
3. Paul-André Monney
Pages 39-57
4. Paul-André Monney
Pages 59-70
5. Paul-André Monney
Pages 71-95
6. Paul-André Monney
Pages 97-108
7. Paul-André Monney
Pages 109-127
8. Paul-André Monney
Pages 129-135
9. Paul-André Monney
Pages 137-148
10. Back Matter
Pages 149-154

### Introduction

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.

### Keywords

regression valuation value-at-risk

#### Authors and affiliations

• Paul-André Monney
• 1
1. 1.Department of StatisticsPurdue UniversityWest LafayetteUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-51746-4
• Copyright Information Physica-Verlag Heidelberg 2003
• Publisher Name Physica, Heidelberg
• eBook Packages
• Print ISBN 978-3-7908-1527-6
• Online ISBN 978-3-642-51746-4
• Series Print ISSN 1431-1968
• Buy this book on publisher's site
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