This volume is a collection of 32 original papers and two
biographical accounts put together as a Festschrift to Herman
Rubin to honor his diverse and many deep contributions to
mathematical sciences over more than 50 years. The topics of the
original articles touch on the main themes in which Professor
Rubin has contributed, as well as other topics of intense current
activity. This volume contains innovative new methodological
articles on cluster analysis, goodness of fit, likelihood
inference, classification algorithms, and meta analysis. On the
purely theoretical side, there are a number of comprehensive
review articles on fractional Brownian motion, stochastic
integration, de Finetti theorems, admissibility, and estimation
under constraints. Each of these review articles provides
readable glimpses into the current state of the art. Some notable
classic unsolved problems in number theory and random
permutations provide attractive additions to the interesting
landscape of this volume.
The IMS Lecture Notes - Monograph Series vol.45
Table of Contents
Stein's method is one of the most powerful tools for proving
limit theorems with sharp, explicit errors for complex dependent
problems. It is curiously hard to grasp how and why it works
since it avoids both characteristic functions and higher moments.
This book consists of tutorial and survey papers aimed at
teaching Stein's method to non specialists. The book provides a
self contained development with motivation and full proofs. As a
unifying theme, all papers use Stein's approach of exchangeable
pairs. In addition to the usual Poisson and Normal approximations
the book gives applications to convergence of Markov chains on
finite state spaces, to birth and death chains and to empirical
process convergence for the bootstrap. One novel feature is the
development of Stein's method as an adjunct to simulation via
Monte Carlo. Usually, the identities underlying the method give
an explicit error term which is bounded. With the present version
using exchangeable pairs, the error is given as an explicit
expectation for the reversible Markov chain. It can thus be
easily simulated to give improvements to classical approximations.
The authors of various chapters, Persi Diaconis, Jason Fulman,
Gesine Reinert, Susan Holmes, Mark Huber and Charles Stein have
used common notation and worked together to achieve a unified
treatment.
The IMS Lecture Notes - Monograph Series vol.46
Table of Contents
This volume is based on the NSF-CBMS Conference in
Mathematical Sciences "New Horizons in Multiple Comparison
Procedures" held in August 2001at Temple University,
Philadelphia, with Yosef Hochberg as the key speaker. The
conference was organized in response to the sudden upsurge of
research that has taken place in the area of multiple comparisons.
A number of newer ideas have emerged from the recent research
activities that could generate a steady stream of new research.
This volume is a collection of 11 papers, covering a broad range
of topics in Multiple Comparisons, which were invited for the
conference. The goal of this volume is to gain deeper
understanding of these ideas and to promote further research
activities in this area.
The IMS Lecture Notes - Monograph Series vol.47
Table of Contents
The analysis of data with outcomes measured repeatedly on each
subject has experienced several transforming developments in the
last twenty years. This monograph presents a unified treatment of
modern methods for longitudinal and/or correlated data that have
developed during this period. The basic approach that the author
takes to modeling longitudinal data is to extend familiar
univariate regression models to multivariate or correlated
outcomes. The author deals with linear models for measured data
and generalized linear models for binary and count data. The
author shows how methods can accommodate missing outcomes and/or
unbalanced designs. Both likelihood and moment methods of
estimation are covered, as are random effects approaches to data
modeling and parameter estimation. The monograph assumes that the
reader has a solid foundation in statistical inference, linear
and generalized linear regression models, and a basic knowledge
of multivariate methods. It is appropriate for second year
doctoral students or postdoctoral fellows in Statistics/Biostatistics
as well as researchers or faculty interested in learning about
the field.
NSF-CBMS Regional Conference Series in Probability and
Statistics,vol.8.
Table of Contents
ISBN: 0-470-02298-1 Paperback
ISBN: 0-470-02297-3 Hardcover
304 pages,May 2005
Description
Statistics: An Introduction Using R offers a concise introduction
to statistical methods, stressing the graphical investigation of
data, and features step-by-step instructions to help the non-statistician
to understand fully the methodology. The computing is done in R,
the freeware version of S-Plus, which is globally recognised as
one of the most powerful and flexible statistical software
packages. This book is the first available title on the market to
cover a broad array of statistical methods at a suitable level
for a wide range of disciplines.
Table of Contents
Preface.
Chapter 1 Fundamentals.
Chapter 2 Dataframes.
Chapter 3 Central Tendency.
Chapter 4 Variance.
Chapter 5 Single Samples.
Chapter 6 Two Samples.
Chapter 7 Statistical Modelling.
Chapter 8 Regression.
Chapter 9 Analysis of Variance.
Chapter 10 Analysis of Covariance.
Chapter 11 Multiple Regression.
Chapter 12 Contrasts.
Chapter 13 Count Data.
Chapter 14 Proportion Data.
Chapter 15 Death and Failure Data.
Chapter 16 Binary Response Variable.
Appendix 1: Fundamentals of the R Language.
ISBN: 0-471-68299-3 Hardcover
560 pages January 2005
Description
Following an innovative approach to learning, this text
integrates paper and pencil skill building and the theoretical
development of ideas with geometric exploration and conceptual
understanding.
Tutorials and traditional text. Visual Linear Algebra covers the
topics in a standard one-semester introductory linear algebra
course in forty-seven sections arranged in eight chapters. In
each chapter, some sections are written in a traditional textbook
style and some are tutorials designed to be worked through using
either Maple or Mathematica.
About the tutorials Each tutorial is a self-contained treatment
of a core topic or application of linear algebra that a student
can work through with minimal assistance from an instructor. The
thirty tutorials are provided on the accompanying CD both as
Maple worksheets and as Mathematica notebooks. They also appear
in print as sections of the textbook.
Geometry is used extensively to help students develop their
intuition about the concepts of linear algebra.
Applications. Students benefit greatly from working through an
application, if the application captures their interest and the
materials give them substantial activities that yield worthwhile
results. Ten carefully selected applications have been developed
and an entire tutorial is devoted to each of them.
Active Learning. To encourage students to be active learners, the
tutorials have been designed to engage and retain their interest.
The exercises, demonstrations, explorations, visualizations, and
animations are designed to stimulate studentsa ? interest,
encourage them to think clearly about the mathematics they are
working through, and help them check their comprehension.
Table of Contents
Chapter 1. Systems of Linear Equations.
Chapter 2. Vectors.
Chapter 3. Matrix Algebra.
Chapter 4. Linear Transformations.
Chapter 5. Vectors Spaces.
Chapter 6. Determinants.
Chapter 7. Eigenvalues and Eigenvectors.
Chapter 8. Orthogonality.
Appendix A: Glossary of Linear Algebra Definitions.
Appendix B: Linear Algebra Theorems.
Appendix C: Advice for Using Maple with Visual Linear Algebra.
Appendix D: Commands Used in Maple Tutorials.
Appendix E: Appendix with Visual Linear Algebra.
Appendix F: Commands Used in Mathematic Tutorials.
Appendix G: Answers and Hints for Selected Pencil and Paper
Problems.
ISBN: 0-471-44459-6 Hardcover
626 pages April 2005
Description
Written by one of the foremost experts in the field, The History
of Mathematics: A Brief Course is substantially revised in the
second edition. This acclaimed text now reorganized topically
rather than geographically begins with first applications of
counting and numbers in the ancient world, and continues with
discussions of geometry, algebra, analysis, probability, logic,
and more. Discussions of women in the history of mathematics make
this a very thorough, inclusive resource.
Table of Contents
Preface to the Second Edition.
PART 1: THE WORLD OF MATHEMATICS AND THE MATHEMATICS OOF THE
WORLD.
Chapter 1. The OPrigin and Prehistory of Mathematics.
Chapter 2. Mathematical Cultures I.
Chapter 3. Mathematical Cultures II.
Chapter 4. Women Mathematicians.
PART 2: NUMBERS.
Chapter 5.Counting.
Chapter 6. Calculation.
Chapter 7. Ancient Number Theory.
Chapter 8. Numbers and Number Theory in Modren Mathematics.
PART 3: COLOR PLATES.
PART 4: SPACE.
Chapter 9. Measurement.
Chapter 10. Euclidean Geometry.
Chapter 11. Post-Euclidean Geometry.
Chapter 12. Modern Geometries.
PART 5: ALGEBRA.
Chapter 13. Prolems Leading to Algebra.
Chapter 14. Equations and Methods.
Chapter 15. Modern Algebra.
PART 6: ANALYSIS.
Chapter 16. The Calculus.
Chapter 17. Real and Complex Aanlysis.
PART 7: MATHEMATICAL INFERENCES.
Chapter 18. Probability and Statistics.
Chapter 19. Logic and Set Theory.
Literature.
Subject Index.
Name Index.