Yuval Z Flicker (The Ohio State University, USA)

AUTOMORPHIC REPRESENTATIONS OF LOW RANK GROUPS

The area of automorphic representations is a natural continuation of studies in number theory and modular forms. A guiding principle is a reciprocity law relating the infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called "liftings". This book concentrates on two initial examples: the symmetric square lifting from SL(2) to PGL(3), reflecting the 3-dimensional representation of PGL(2) in SL(3); and basechange from the unitary group U(3, E/F) to GL(3, E), [E : F] = 2.
The book develops the technique of comparison of twisted and stabilized trace formulae and considers the “Fundamental Lemma” on orbital integrals of spherical functions. Comparison of trace formulae is simplified using "regular" functions and the "lifting" is stated and proved by means of character relations.

This permits an intrinsic definition of partition of the automorphic representations of SL(2) into packets, and a definition of packets for U(3), a proof of multiplicity one theorem and rigidity theorem for SL(2) and for U(3), a determination of the self-contragredient representations of PGL(3) and those on GL(3, E) fixed by transpose-inverse-bar. In particular, the multiplicity one theorem is new and recent.

There are applications to construction of Galois representations by explicit decomposition of the cohomology of Shimura varieties of U(3) using Deligne's (proven) conjecture on the fixed point formula.

Contents:

On the Symmetric Square Lifting:
Functoriality and Norms
Orbital Integrals
Twisted Trace Formula
Total Global Comparison
Applications of a Trace Formula
Computation of a Twisted Character
Automorphic Representations of the Unitary Group U(3, E/F):
Local Theory
Trace Formula
Liftings and Packets
Zeta Functions of Shimura Varieties of U(3):
Automorphic Representations
Local Terms
Real Representations
Galois Representations

Readership: Graduate students and researchers in number theory, algebra and representation theory.

500pp Pub. date: Jun 2006
ISBN 981-256-803-4

Michael Greenacre / Universitat Pompeu Fabra, Barcelona, Spain
Jorg Blasius / University of Bonn, Germany

Multiple Correspondence Analysis and Related Methods

Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Scien Volume: 1

ISBN: 1584886285
Publication Date: 6/23/2006
Number of Pages: 608

Provides the first comprehensive overview of the theory and applications of MCA
Begins with two chapters that gently introduce the method to those with less experience in the field
Adopts a practical approach with many worked examples
Includes applications in survey research, social sciences, marketing, health economics, and biomedical research
Features software notes in each chapter, an appendix with computational details, and R programs for applying methods

As a generalization of simple correspondence analysis, multiple correspondence analysis (MCA) is a powerful technique for handling larger, more complex datasets, including the high-dimensional categorical data often encountered in the social sciences, marketing, health economics, and biomedical research. Until now, however, the literature on the subject has been scattered, leaving many in these fields no comprehensive resource from which to learn its theory, applications, and implementation.

Multiple Correspondence Analysis and Related Methods gives a state-of-the-art description of this new field in an accessible, self-contained, textbook format. Explaining the methodology step-by-step, it offers an exhaustive survey of the different approaches taken by researchers from different statistical "schools" and explores a wide variety of application areas. Each chapter includes empirical examples that provide a practical understanding of the method and its interpretation, and most chapters end with a "Software Note" that discusses software and computational aspects. An appendix at the end of the book gives further computing details along with code written in the R language for performing MCA and related techniques. The code and the datasets used in the book are available for download from a supporting Web page.

Providing a unique, multidisciplinary perspective, experts in MCA from both statistics and the social sciences contributed chapters to the book. The editors unified the notation and coordinated and cross-referenced the theory across all of the chapters, making the book read seamlessly. Practical, accessible, and thorough, Multiple Correspondence Analysis and Related Methods brings the theory and applications of MCA under one cover and provides a valuable addition to your statistical toolbox.

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Anthony O'Hagan, Caitlin E. Buck, Alireza Daneshkhah, Richard Eiser,
Paul Garthwaite, David Jenkinson, Jeremy Oakley, Tim Rakow

Uncertain Judgements: Eliciting Experts' Probabilities

ISBN: 0-470-02999-4
Hardcover
338 pages
September 2006

An aim of much statistical research is to wring as much from data as is possible. Improved usage of expert opinion can add significantly more information than a slight improvement in efficiency through better data analysis techniques. This book presents a range of tried and tested elicitation methods to enable statisticians to get make the most of expert opinion
An elicitation method forms a bridge between an expert’s opinion and an expression of these points in a statistically useful form. This book, written by a group of expert statisticians and psychologists provides an introduction to the subject and a detailed overview of the existing literature. The book guides the reader through the design of an elicitation method and details examples from a cross section of literature in the statistics, psychology, engineering and health sciences disciplines.

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Andrew R. Willan, Andrew H. Briggs

Statistical Analysis of Cost-Effectiveness Data

ISBN: 0-470-85626-2
Hardcover
210 pages
September 2006


The statistical analysis of cost-effectiveness data is becoming increasingly important within health and medical research. Statistical Analysis of Cost-Effectiveness Data provides a practical book that synthesises the huge amount of research that has taken place in the area over the last two decades.
Comprising an up-to-date overview of the statistical analysis of cost-effectiveness data, the book is supported by numerous worked examples from the author’s own experience. It has been written in a style suitable for medical statisticians and health care professionals alike. Key features include:

an overview of statistical methods used in the analysis of cost-effectiveness data.
coverage of Bayesian methodology.
illustrated throughout by worked examples using real data.
suitability for health care professionals with limited statistical knowledge.
discussion of software used for data analysis.
An essential reference for biostatisticians and health economists engaged in cost-effectiveness analysis of health-care interventions, both in academia and industry. Also of interest to graduate students of biostatistics, public health and economics.

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