A mathematical theory of arguments for statistical evidence
type: Item
instance of: scholarly article
title: A mathematical theory of arguments for statistical evidence
zbMATH Open document ID: 1100.62005
author: P. A. Monney
published in: Contributions to Statistics
publication date: 2003-02-16T00:00:00Z
review text: The book, clearly written, is structured in two parts comprising two and six chapters, respectively. The first part addresses the problem of modeling reasoning through the use of functional models involving discrete spaces. The underlying theory of such models provides insight for the weighing of evidence. The second part treats the case of special linear functional models, termed Gaussian linear models in continuous spaces. The theory of hints has a central role throughout the book and the presented material aims at providing hints permitting the evaluation of some hypotheses of interest. Chapter 1 contains a presentation of the theory of generalized functional models, which through several examples are demonstrated to be useful tools in modeling reasoning under uncertainty. The reader is first provided with a concise introduction to the theory of hints and its most prominent concepts and properties appropriate to measuring the effect of assumption-based reasoning on functional models. In chapter 2, the notion of likelihood is extended to composite hypotheses in terms of the plausibility function of some hint obtained from a generalized functional model allowing the definition of a general weight of evidence applicable to both simple and composite hypotheses. The chapters that follow comprising the second part of the book, are devoted to special linear functional models involving continuous spaces. Starting with chapter 3, a theory of continuous hints is presented through a formal exposition. These have all the characteristics of hints on finite frames only adapted for continuous ones. A class of Gaussian linear models is also defined. These are generalized functional models of a special form. Chapter 4 treats the principle of assumption-based reasoning through the prism of a special class of Gaussian linear systems, which coincide with classical regression models with known error term when expressed in canonical coordinates. The information generated about the par…
reviewed by: Evdokia Xekalaki
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 68T37
Mathematics Subject Classification ID: 68-02
zbMATH DE Number: 1868963
zbMATH Keywords: statistical evidence
zbMATH Keywords: logic
zbMATH Keywords: statistical inference
zbMATH Keywords: linear models
zbMATH Keywords: Kalman filter
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1868963