Description
Categorical data-comprising counts of individuals, objects, or
entities in different categories-emerge frequently from many
areas of study, including medicine, sociology, geology, and
education. They provide important statistical information that
can lead to real-life conclusions and the discovery of fresh
knowledge. Therefore, the ability to manipulate, understand, and
interpret categorical data becomes of interest-if not
essential-to professionals and students in a broad range
ofdisciplines.
Although t-tests, linear regression, and analysis of variance are
useful, valid methods for analysis of measurement data,
categorical data requires a different methodology and techniques
typically not encountered in introductory statistics courses.
Developed from long experience in teaching categorical analysis
to a multidisciplinary mix of undergraduate and graduate
students, A Course in Categorical Data Analysis presents the
easiest, most straightforward ways of extracting real-life
conclusions from contingency tables. The author uses a Fisherian
approach to categorical data analysis and incorporates numerous
examples and real data sets. Although he offers S-PLUS routines
through the Internet, readers do not need full knowledge of a
statistical software package. In this unique text, the author
chooses methods and an approach that nurtures intuitive thinking.
He trains his readers to focus not on finding a model that fits
the data, but on using different models that may lead to
meaningful conclusions. The book offers some simple, innovative
techniques not highighted in other texts that help make the book
accessible to a broad, interdisciplinary audience. A Course in
Categorical Data Analysis enables readers to quickly use its
offering of tools for
drawing scientific, medical, or real-life conclusions from
categorical data sets.
Audience
Professionals and students in Mathematics, Statistics, Social
Sciences, Economics, Medicine, Business, and Actuarial Science
Researchers in these and other areas, including education,
psychology, and biology
Contents
S-PLUS Routines
Sampling Distributions
Experimental Design for a Population Proportion
Further Properties of the Binomial Distribution
Estimation, Inference, and Hypothesis Testing for the Binomial
Distribution
The Poisson Distributions: Its Characterizations and Properties
Estimation, Inference, and Hypothesis Testing for the Poisson
Distribution
The Multinomial distribution
Sir Ronald Fisher's Conditioning Result
More general Sampling Models
Generalizing the Binomial Distribution
The Discrete Exponential Facility of Distribution
Generalizing the Multinomial Distribution
Two by Two Contingency Tables
Conditional Probability and Independence
Independence of Rows and columns
Investigating Independence, Give Observational Data
Edwards' Theorem
Log Contrasts and the Multinomial Distribution
The Log Measure of Association Test (Single Multinomial Model)
The Product Binomial
The Independent Poisson Model
Fisher's Exact Test
Power Properties of our Test Procedures
Simpson's Paradox and 23 Tables
Probability Theory
The Cornish Pixie: Irish Leprechaun Example
Interpretation of Simpson's Paradox
The Three-Directional Approach
Measure of Association Analysis for 23 Tables
Medical Example
The Madison Drug Alcohol Abuse Study
Experimental Design and Data Collection
Sensitivity and Specificity
Analysis of Results
Goodman's Full Rank Interaction Analyzed for Two Way Tables
Introductory Example
Methodological Development
Numerical Example
Methodological Developments
Business School Example
Methodological Developments
Advertising Example
Testing for Equality of Unconditional Cell Probabilities of
Several r x s Tables
Analysis of Berkeley Admissions Data
Further Data Sets
Further Examples
Further Examples and Extensions
A Three-Way Table-Hypertension Obesity, and Alcohol Consumption
The Bristol Cervical Smear Data
Higher Grade Results for Eight Moray Secondary Schools
Further Data Sets
Conditional Independence Models for Two-Way Tables
Fixed Zeros and Missing Observations
Conditional Independence in Incomplete Tables
Perfectly Fitting Further Cells
Conditional Independence in Complete Tables
Further Data
Logistic Regression
Review of General Methodology
Analyzing Your Data Using S-PLUS
Analysis of Mice Exposure Data
Generalized Linear Models
A Generalized Linear Model for Poisson Data
A Generalized Linear Model for Point Processes
Analysis Using Splus
Extending Generalized Linear Models for Poisson Counts
Further Topics
Logistic Discrimination Analysis
Medical Examples
Three-Way Contingency Tables
Features
+ Details the most useful methods for extracting information and
drawing meaningful conclusions from categorical data
+ Uses a direct approach from a Fisherian viewpoint
+ Encourages intuitive thinking
+ Includes simple, innovative methods not highlighted in other
texts
ISBN: 1584881801
Publication Date: 11/24/99
Edited by Richard C. Jeffrey
Introductions and Afterword by John P. Burgess
George Boolos was one of the most prominent and influential
logician-philosophers of recent times. This
collection, nearly all chosen by Boolos himself shortly before
his death, includes thirty papers on set theory,
second-order logic, and plural quantifiers; on Frege, Dedekind,
Cantor, and Russell; and on miscellaneous
topics in logic and proof theory, including three papers on
various aspects of the G?del theorems. Boolos is
universally recognized as the leader in the renewed interest in
studies of Frege's work on logic and the
philosophy of mathematics. John Burgess has provided
introductions to each of the three parts of the
volume, and also an afterword on Boolos's technical work in
provability logic, which is beyond the scope of
this volume.
George Boolos was Professor of Philosophy, Massachusetts
Institute of Technology, author of The Logic of
Provability, and coauthor of Computability and Logic.
Contents
I Studies on Set Theory and the Nature of Logic
Introduction to Part I
The Iterative Conception of Set
Reply to Charles Parsons's "Sets and Classes"
On Second-Order Logic
To Be Is to Be a Value of a Variable (Or to Be Some Values of
Some Variables)
Nominalist Platonism
Iteration Again
Introductory Notes to G?del *1951
Must We Believe in Set Theory?
II Frege Studies
Introduction to Part II
Gottlob Frege and the Foundations of Arithmetic
Reading the Begriffsschrift
Saving Frege from Contradiction
The Consistency of Frege's Foundations of Arithmetic
The Standard of Equality of Numbers
Whence the Contradiction?
1879?
The Advantages of Honest Toil over Theft
On the Proof of Frege's Theorem
Frege's Theorem and the Peano Postulates
Is Hume's Principle Analytic?
Die Grundlagen der Arithmetik, 82-83 (with Richard Heck)
Constructing Cantorian Counterexamples
III Various Logical Studies and Lighter Papers
Introduction to Part III
Zooming Down the Slippery Slope
Don't Eliminate Cut
The Justification of Mathematical Induction
A Curious Inference
A New Proof of the G?del Incompleteness Theorem
On "Seeing" the Truth of the G?del Sentence
Quotational Ambiguity
The Hardest Logical Puzzle Ever
Godel's Second Incompleteness Theorem Explained in Words of One
Syllable
October 1999
6 x 9 inches
First cloth edition: Spring 1998
11 line illustrations, 2 tables
448 pages
ISBN 0-674-53767-X
L. C. G. ROGERS / University of Bath
AND D. WILLIAMS /University of Bath, UK
Description: Now available in paperback, this celebrated book has
been prepared with readers' needs in mind, remaining a systematic
guide to a large part of the modern theory of Probability, whilst
retaining its vitality. The authors' aim is not just to present
the subject of Brownian motion as a dry part of mathematical
analysis, but to convey its real meaning and fascination. The
opening, heuristic chapter does just this, and it is followed by
a comprehensive and self-contained account of the foundations of
theory of stochastic processes. Chapter 3 is a lively and
readable account of the theory of Markov processes. Together with
its companion volume, this book helps equip graduate students for
research into a subject of great intrinsic interest and wide
application in physics, biology, engineering, finance and
computerscience.
Contents: Some frequently used notation; 1. Brownian motion; Part
I. Introduction; 2. Basics about Brownian motion; 3. Brownian
motion in higher dimensions; 4. Gaussian processes and L?vy
processes; Part II. Some Classical Theory; 5. Basic measure
theory; 6. Basic probability theory; 7. Stochastic processes; 8.
Discrete-parameter martingale theory; 9. Continuous-parameter
martingale theory; 10. Probability measure on Lusin spaces; Part
III. Markov Processes: 11. Transition functions and resolvents;
12. Feller-Dynkin processes; 13. Additive functionals; 14.
Approach to ray processes: the Martin boundary; 15. Ray
processes; 16. Applications;References; Index.
Essential Information
ISBN, Binding, Price: 0521775949 Paperback
Approximate Publication date: 29 February 2000
Main Subject Category: Mathematics - analysis, probability
2000 228 x 152 mm 406pp 49 exercises
L. C. G. ROGERS / University of Bath
AND D. WILLIAMS / University of Bath
Description: Now available in paperback, this celebrated book
has been prepared with readers' needs in mind, remaining a
systematic treatment of the subject whilst retaining its
vitality. The second volume follows on from the first,
concentrating on stochastic integrals, stochastic differential
equations, excursion theory and the general theory of processes.
Much effort has gone into making these subjects as accessible as
possible by providing many concrete examples that illustrate
techniques of calculation, and by treating all topics from the
ground up, starting from simple cases. Many of the examples and
proofs are new; some important calculational techniques appeared
for the first time in this book. Together with its companion
volume, this book helps equip graduate students for research into
a subject of great intrinsic interest
and wide application in physics, biology, engineering, finance
and computer science.
Contents: Some frequently used notation; 4. Introduction to Ito
calculus; 4.1. Some motivating remarks; 4.2. Some fundamental
ideas: previsible processes, localization, etc.; 4.3. The
elementary theory of finite-variation processes; 4.4 . Stochastic
integrals: the L2 theory; 4.5. Stochastic integrals with respect
to continuous semimartingales; 4.6. Applications of Ito's
formula; 5. Stochastic differential equations and diffusions;
5.1. Introduction; 5.2. Pathwise uniqueness, strong SDEs, flows;
5.3. Weak solutions, uniqueness in law; 5.4. Martingale problems,
Markov property; 5.5. Overture to stochastic differential
geometry; 5.6. One-dimensional SDEs; 5.7. One-dimensional
diffusions; 6. The general theory; 6.1. Orientation; 6.2. Debut
and section theorems; 6.3. Optional projections and filtering;
6.4. Characterising previsible times; 6.5. Dual previsible
projections; 6.6. The Meyer decomposition theorem; 6.7.
Stochastic integration; the general case; 6.8. Ito excursion
theory; References; Index.
Essential Information
ISBN, Binding, Price: 0521775930 Paperback 5
Approximate Publication date: 1 March 2000
Main Subject Category: Mathematics - analysis, probability
2000 228 x 152 mm 490pp
Hans von Storch /GKSS Research Centre, Geesthacht
and Francis W. Zwiers /Canadian Centre for Climate Modelling and
Analysis, Victoria
Description
Climatology is, to a large degree, the study of the statistics of
our climate. The powerful tools of mathematical statistics
therefore find wide application in climatological research. The
purpose of this book is to help the climatologist
understand the basic precepts of the statisticians art and to
provide some of the background needed to apply statistical
methodology correctly and usefully. The book is self contained:
introductory material, standard advanced techniques,
and the specialised techniques used specifically by
climatologists are all contained within this one source. There
are a wealth of real-world examples drawn from the climate
literature to demonstrate the need, power and pitfalls
of statistical analysis in climate research. Suitable for
graduate courses on statistics for climatic, atmospheric and
oceanic
science, this book will also be valuable as a reference source
for researchers in climatology, meteorology, atmospheric
science, and oceanography.
Chapter Contents
Prologue; 1. Introduction; Part I. Fundamentals: 2. Probability
theory; 3. Distributions of climate variables; 4.
Concepts in statistical inference; 5. Estimation; Part II.
Confirmation and Analysis: 6. The statistical test of a
hypothesis; 7. Analysis of atmospheric circulation problems; Part
III. Fitting Statistical Models: 8. Regression; 9.
Analysis of variance; Part IV. Time Series: 10. Time series and
stochastic processes;
11. Parameters of univariate and bivariate time series; 12.
Estimation of covariance functions and spectra; Part V. Eigen
Techniques: 13. Empirical orthogonal functions; 14. Canonical
correlation analysis; 15. Principal oscillation pattern
analysis; 16. Complex eigentechniques; Part VI. Other Topics: 17.
Specific statistical concepts in climate research; 18.
Forecast quality evaluation; Part VII.
Appendices.
Title Details
Binding: Hardback
Bibliographic information:
276 x 219 mm 494pp 229 line diagrams 2
half-tones 14 tables
ISBN: 0 521 45071 3
15 July 1999
Mitchell H. Katz / University of California, San Francisco
Description
Multivariable analysis is a challenging subject for clinicians,
whether they are novice researchers or trained
practitioners. Most biostatistics books do not cover
multivariable analysis, while existing multivariable
analysis books are dense with mathematical formulas.
Multivariable Analysis: A Practical Guide for
Clinicians steps aside from mathematics to offer conceptual
explanations. Dr Mitchell Katz
follows a non-threatening, question-and-answer approach to
explain how to perform and interpret
multivariable analyses. He begins by explaining why clinicians
should do multivariable analysis and then guides
them through topics such as how to choose multivariable methods,
analyse independent variables, and
validate multivariable models. The book is loaded with useful
tips, tables, figures, and references and
examples from medical literature demonstrate real-world
applications and uses of multivariable analysis.
Multivariable Analysis: A Practical Guide for Clinicians is an
indispensable guide for medical
students, residents, and practisingphysicians.
Chapter Contents
1. Introduction; 2. Common uses of multivariable models; 3.
Outcome variables in multivariable analysis; 4.
Independent variables in multivariable analysis; 5. Assumptions
of multiple linear
regression, logistic regression, and proportional hazard
analysis; 6. Relationship of independent
variables to one another; 7. Setting up a multivariable analysis:
subjects; 8. Performing the analysis; 9.
Interpreting the analysis; 10. Checking the assumptions of the
analysis; 11. Validation of models;
12. Special topics; 13. Publishing your study; 14. Summary: steps
for constructing a multivariable model.
Title Details
Binding: Hardback
Bibliographic information:
234 x 156 mm 208pp 26 line diagrams 34 tables
ISBN: 0 521 59301 8
01 July 1999
An Introduction to the Casson Invariant
1999. 24 x 17 cm. IX, 199 pages. With 134 figures.
Hardcover.
ISBN 3-11-016272-5
Paper.
ISBN 3-11-016271-7
Progress in low-dimensional topology has been very fast in the
last two decades, leading to the solutions of many difficult
problems.
One of the consequences of this ?acceleration of historyg is
that many results have only appeared in professional journals and
monographs. These are hardly accessible to students who have
completed only a basic course in algebraic topology, or even to
some
researchers whose immediate area of expertise is not topology.
Among the highlights of this period are Casson's results on the
Rohlin invariant of homotopy 3-spheres, as well as his
$\lambda$-invariant. The purpose of this book is to provide a
much-needed bridge to these modern topics. The book covers some
classical topics, such as Heegaard splittings, Dehn surgery, and
invariants of knots and links. It proceeds through the Kirby
calculus
and Rohlin's theorem to Casson's invariant and its applications,
and gives a brief sketch of links with the latest developments in
low-dimensional topology and gauge theory.
The text will be accessible to graduate students in mathematics
and theoretical physics familiar with some elementary algebraic
topology, including the fundamental group, basic homology theory,
and Poincar? duality on manifolds.
A.V. Bolsinov
Faculty of Mechanics and Mathematics, Moscow State University,
Russia
A.T. Fomenko
Dept. of Mathematics and Mechanics, Moscow State University,
Russia
MONOGRAPHS IN CONTEMPORARY MATHEMATICS
Presenting a new approach to qualitative analysis of integrable
geodesic flows based on the theory of topological classification
of integrable Hamiltonian systems, this is the first book to
apply this technique systematically to a wide
class of integrable systems.
The first part of the book provides an introduction to the
qualitative theory of integrable Hamiltonian systems and their
invariants (symplectic geometry, integrability, the topology of
Liouville foliations, the orbital classification theory for
integrable nondegenerate Hamiltonian systems with two degrees of
freedom, obstructions to integrability, etc).
In the second part, the class of integrable geodesic flows on
two-dimensional surfaces is discussed both from the classical and
contemporary point of view. The authors classify them up to
different equivalence relations such as an isometry, the
Liouville equivalence, the trajectory equivalence (smooth and
continuous), and the geodesic equivalence. A new technique, which
provides the possibility to classify integrable geodesic flows up
to these kinds of equivalences, is presented together with
applications.
Together with systematic presentation of wide material on this
subject, the book contains previously unpublished new results,
and is enhanced with manyoriginal illustrations.
Contents
Preface. 1. Basic Notions. 2. Topology of Foliations Generated by
Morse
Functions on Two-Dimensional Surfaces. 3. Rough Liouville
Equivalence of
Integrable Systems with Two Degrees of Freedom. 4. Liouville
Equivalence of
Integrable Systems with Two Degrees of Freedom. 5. Trajectory
Classification
of Integrable Systems with Two Degrees of Freedom. 6. Integrable
Geodesic
Flowson Two-Dimensional Surfaces. 7. Liouville Classification of
Integrable
Geodesic Flows on Two-Dimensional Surfaces. 8. Trajectory
Classification of
Integrable Geodesic Flows on Two-Dimensional Surfaces. 9.
Maupertuis
Principle and Geodesic Equivalence. 10. Euler Case in Rigid Body
Dynamics
and Jacob Problem About Geodesics on the Ellipsoid. Trajectory
Isomorphism.
References.
Kluwer Academic/Plenum Publishers
Hardbound, ISBN 0-306-11065-2
January 2000, 332 pp.
edited by
Ad?lia Sequeira/ I.S.T., Technical University, Lisbon, Portugal
Hugo Beir?o da Veiga /University of Pisa, Italy
Juha H. Videman /I.S.T., Technical University, Lisbon, Portugal
Proceedings of an International Workshop on Nonlinear PDEs and
Applications, held December 13-17, 1999, in Olomouc, Czech
Republic, in honour of the 70th birthday of Professor Jindrich
Necas
This book gives up to date information on a variety of topics
within the field of applied nonlinear analysis. With
contributions from a number of world-wide authorities, it
includes articles on Navier-Stokes equations, nonlinear
elasticity, non-Newtonian fluids, regularity of solutions of
parabolic and elliptic equations, operator theory and numerical
methods.
Contents and Contributors
On the regularity and decay of the weak solutions to the
steady-state Navier-Stokes equations in exterior domains; F.
Alliot, C. Amrouche. A note on turbulence modeling; G.Q. Chen, et
al. L2,l Eregularity for nonlinear elliptic systems of second
order; J. Danec, E. Viszus. On the Fredholm alternative for
nonlinear homogeneous operators; P. Dr?bek. Existence of
solutions to a nonlinear coupled thermo-viscoelastic contact
problem with small Coulomb friction; C. Eck, J. Jarusek. On some
global existence theorems for a semilinear parabolic problem;
Y.V. Egorov, V.A. Kondratiev. Bifurcation of solutions to
reaction-diffusion systems with jumping nonlinearities; J.
Eisner,
M. Kucera. Coupled problems for viscous incompressible flow in
exterior domains; M. Feistauer, C. Schwab. Remarks on the
determinant in nonlinear elasticity and fracture mechanics; I.
Fonseca, J. Mal?. On modelling of Czochralski flow, the case of
non plane free surface; J. Franc?. Symmetric stationary solutions
to the plane exterior Navier-Stokes problem for arbitrary large
Reynolds number; G.P. Galdi. A fictitious-domain method with
distributed multiplier for the Stokes problem; V. Girault, et al.
Reliable solution of a unilateral contact problem with friction,
considering uncertain input data; I. Hlav?cek. Domain
decomposition algorithm for computer aided design; F. Hecht, et
al. Solution of convection-diffusion problems with the memory
terms; J. Kacur. On global existence of smooth two-dimensional
steady flows
for a class of non-Newtonian fluids under various boundary
conditions; P. Kaplick?, et al. Viscosity solutions for
degenerate and nonmonotone elliptic equations; B. Kawohl, N.
Kutev. Remarks on compactness in the formation of fine
structures; P. Kloucek. Finite element analysis of a nonlinear
elliptic problem with a pure radiation condition; M. Kr?zek, et
al. Estimates of three-dimensional Oseen kernels in weighted Lp
spaces; S. Kracmar, et al. Hardy's inequality and spectral
problems of nonlinear operators; A. Kufner. Remarks on the
regularity of solutions of elliptic systems; S. Leonardi.
Singular perturbations in optimal control problem; J. Lov?sek.
Optimization of steady flows for incompressible viscous fluids;
J. M?lek, T. Roub?cek. Asymptotic behaviour of compressible
Maxwell fluids in exterior domains; S. Matusu-Necasov?, et al.
Regularity of a suitable weak solution to the Navier-Stokes
equations as a consequence of regularity of one velocity
component, J. Neustupa, P. Penel. On a class of high resolution
methods for solving hyperbolic conservation laws with source
terms; P. de Oliveira, J.
Santos. On the decay to zero of the L2-norms of perturbations to
a viscous compressible fluid motion exterior to a compact
obstacle; M. Padula. Global behavior of compressible fluid with a
free boundary and large data; P. Penel, I. Straskraba. A
geometric approach to dynamical systems in IRn; R. Rautmann. On a
three-dimensional convective Stefan problem for a non-Newtonian
fluid;
J.F. Rodrigues, J.M. Urbano. Replacing h by h2; M. Rokyta. Flow
of shear dependent electrorheological fluids: unsteady space
periodic case; M. Ruzicka. On decay of solutions to the
Navier-Stokes equations; M.E. Schonbek. Convexity conditions for
rotationally invariant functions in two dimensions; M. Silhav?.
H?lder continuity of weak solutions to nonlinear parabolic
systems in two space dimensions; J. Wolf.
Kluwer Academic/Plenum Publishers
Hardbound, ISBN 0-306-46303-2
October 1999, 576 pp.
Edited by: B. V. Rajarama Bhat, Indian
Statistical Institute, Bangalore, India, George A. Elliott,
University of Toronto, ON, Canada,
and Peter A. Fillmore, Dalhousie University, Halifax, NS, Canada
Description
This book resulted from the lectures held at The Fields Institute
(Waterloo, ON, Canada). Leading international experts presented
current results on the theory of $C^*$-algebras and von Neumann
algebras, together with recent work on the classification of
$C^*$-algebras. Much of the material in the book is appearing
here for the first time and is not available elsewhere in the
literature.
Contents
C*-algebras
C*-algebras: Definitions and examples
C*-algebras: Constructions
Positivity in C*-algebras
K-theory I
Tensor products of C*-algebras
Crossed products I
Crossed products II: Examples
Free products
K-theory II: Roots in topology and index theory
C*-algebraic K-theory made concrete or trick or treat with $2
\times 2$ matrix algebras
Dilation theory
C*-algebras and mathematical physics
C*-algebras and several complex variables
von Neumann algebras
Basic structure of von Neumann algebras
von Neumann algebras (Type $II_1$ factors)
The equivalence between injectivity and hyperfiniteness, part I
The equivalence between injectivity and hyperfiniteness, part II
On the Jones index
Introductory topics on subfactors
The Tomita-Takesaki theory explained
Free products of von Neumann algebras
Semigroups of endomorphisms of $\Cal{B}(H)$
Classification of C*-algebras
AF-algebras and Bratteli diagrams
Classification of amenable C*-algebras I
Classification of amenable C*-algebras II
Simple AI-algebras and the range of the invariant
Classification of simple purely infinite C*-algebras I
Hereditary subalgebras of certain simple non real rank zero
C*-algebras
Preface
Introduction
The isomorphism theorem
The range of the invariant
Bibliography
Paths on Coxeter diagrams: From platonic solids and singularities
to minimal models and subfactors
Preface/Acknowledgements
The Kauffman-Lins recoupling theory
Graphs and connections
An extension of the recoupling model
Relations to minimal models and subfactors
Bibliography
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Fields Institute Monographs, Volume: 13
Publication Year: 2000
ISBN: 0-8218-0821-4
Paging: 323 pp.
Binding: Hardcover