Bayesian methods combine information available from data with any
prior information available from expert knowledge. The Bayes linear
approach follows this path, offering a quantitative structure for
expressing beliefs, and systematic methods for adjusting these
beliefs, given observational data. The methodology differs from the
full Bayesian methodology in that it establishes simpler approaches
to belief specification and analysis based around expectation
judgements. Bayes Linear Statistics presents an
authoritative account of this approach, explaining the foundations,
theory, methodology, and practicalities of this important field.
The text provides a thorough coverage of Bayes linear analysis,
from the development of the basic language to the collection of
algebraic results needed for efficient implementation, with
detailed practical examples.
The book covers:
* The importance of partial prior specifications for complex
problems where it is difficult to supply a meaningful full prior
probability specification.
* Simple ways to use partial prior specifications to adjust
beliefs, given observations.
* Interpretative and diagnostic tools to display the implications
of collections of belief statements, and to make stringent
comparisons between expected and actual observations.
* General approaches to statistical modelling based upon partial
exchangeability judgements.
* Bayes linear graphical models to represent and display partial
belief specifications, organize computations, and display the
results of analyses.
Bayes Linear Statistics is essential reading for all
statisticians concerned with the theory and practice of Bayesian
methods. There is an accompanying website hosting free software and
guides to the calculations within the book.
Inhoudsopgave
Preface.
1 The Bayes linear approach.
2 Expectation.
3 Adjusting beliefs.
4 The observed adjustment.
5 Partial Bayes linear analysis.
6 Exchangeable beliefs.
7 Co-exchangeable beliefs.
8 Learning about population variances.
9 Belief comparison.
10 Bayes linear graphical models.
11 Matrix algebra for implementing the theory.
12 Implementing Bayes linear statistics.
A Notation.
B Index of examples.
C Software for Bayes linear computation.
C.1 [B/D].
C.2 BAYES-LIN.
References.
Index.
Over de auteur
Michael Goldstein, Professor of Statistics, Department of
Mathematical Sciences, University of Durham
Michael Goldstein has worked on and researched the Bayes linear
approach for around 30 years, his general interests being in the
foundations, methodology and applications of Bayesian/subjectivist
approaches to statistics. He has an outstanding reputation as one
of the most original thinkers in the field, and was a contributing
author to Wiley’s ‘Encyclopedia of Statistical
Sciences’.
David Wooff, Director of Statistics & Mathematics
Consultancy Unit and Senior Lecturer in Statistics, Department of
Mathematical Sciences, University of Durham
David Wooff has been involved in a long collaboration for over 20
years with Michael Goldstein and others on developing Bayes linear
methods, his primary research interest being the general
development and application of Bayes linear methodology.
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