Series
Statistics: Textbooks and Monographs series.Volume:
171
Textbook | Print Published: 10/01/2003
Hard Cover
250 pages | Illustrated
Print ISBN: 0-8247-4701-1
Description
Provides a comprehensive description on a
method of constructing
a statistical model when only incomplete
data is available, and
then proposes specific estimation algorithms
for solving various
individual incomplete data problems. Discusses
the realistic
problems on the processing of missing values
commonly seen in
multidimensional data and the various methods
to cope with them.
Table of Contents
Incomplete Data and the Generation Mechanisms
Type of Incomplete Data and its Analysis
Statistical Models for Incomplete Data
Analysis of Data with Missing Values
Missing Data in Multinominal Data
Algorithms for MLE for Multivariate Normal
Data with Missing
Values
Scoring Method
EM Algorithm
Basics of EM Algorithm
Extension of EM Algorithm and Acceleration
EM Algorithm as an Optimization Tool
Robust Model and Outlier Detection
Scale Mixture Model of Normal Distributions
Multivariate and Contaminated Normal Distribution
Robust Tobit Model
Robust Factor Model
Statistical Model with Latent Variables
Latent Structure Model and EM Algorithm
Latent Class Model and Latent Trait Model
Structured Equations Model with Latent Variables
Extensions of EM Algorithm
ECM Algorithm ECME Algorithm
Optimal EM Algorithm
MCEM Algorithm
Covergence Speed of EM Algorithm
Convergence Speed
Comparisons of EM and Other Optimization
Algorithms Quasi Newton
Method
Acceleration Methods of the EM Algorithm
Neural networks and EM algorithm
EM Algorithm in Neural Networks
Geometric Interpretation of EM Algorithm
Marcov Chain Monte Carlo
Bayes Estimation
Marcov Chain
Metropolis-Hastings Algorithm
Data Augmentation Algorithm
Poor Manfs Data Augmentation Algorithm
Gibbs Sampling Algorithm
References
Appendix A: SOLAS for Missing Data Analysis
Appendix B: Lem.
Series
Statistics: Textbooks and Monographs series.Volume:
171
Textbook | Print Published: 10/01/2003
Hard Cover
550 pages | Illustrated
Print ISBN: 0-8247-4713-5
Description
This Second Edition adds new topics in properties
and
characterization of symmetric distribution,
elliptically
symmetric multivariate distributions, singular
symmetric
distributions, estimation of covariance matrices,
tests of mean
against one-sided alternatives, and more.
Draws on multivariate
data from biometry, agriculture, biomedical
sciences, economics,
filtering and stochastic control, stock market
data analysis, and
random signal processing.
Table of Contents
Vector and Matrix Algebra
Groups, Jacobian of Some Transformations,
Functions, and Spaces
Multivariate Distributions and Invariance
Properties of Multivariate Distributions
Estimators of Parameters and Their Functions
Basic Multivariate Sampling Distributions
Tests of Hypotheses of Mean Vectors
Tests Concerning Covariance Matrices and
Mean Vectors
Discriminant Analysis
Principal Components
Canonical Correlations
Factor Analysis
Bibliography of Related Recent Publications
Appendix A: Tables for the Chi-Square Adjustment
Factor
Appendix B: Publications of the Author.
Description
In this book, a comprehensive and up-to-date
review of the area
of Survival Analysis is provided. Important
topics such as
Censored and Truncated Data Analysis, Competing
Risks Analysis,
Proportional Hazards Model, Stochastic Models
in Epidemiology,
and ROC Curve and Analysis, are reviewed
by renowned experts
working in this area of research. The coverage
includes both
theoretical advances as well as applied data
analysis. The
articles are written in a user-friendly manner
and hence will
serve as a useful reference source for researchers
in the area of
Survival Analysis, as well as a guide for
students and
practitioners interested in this area of
research.
Key features:
Includes up-to-date reviews on many important
topics.
Chapters written by many internationally
renowned experts.
Some Chapters provide completely new methodologies
and analyses.
Includes some new data and methods of analyzing
them.
A unique collection of expertly written review
articles covering
all divers aspects of the area of Survival
Analysis.
Audience
Biostatisticans, Mathematical Statisticans,
Reliability Engineers.
Year 2004
Hardbound
ISBN: 0-444-50079-0
1000 pages
North-Holland Mathematics Studies, 193
Description
All the existing books in Infinite Dimensional
Complex Analysis
focus on the problems of locally convex spaces.
However, the
theory without convexity condition is covered
for the first time
in this book. This shows that we are really
working with a new,
important and interesting field.
Theory of functions and nonlinear analysis
problems are
widespread in the mathematical modeling of
real world systems in
a very broad range of applications. During
the past three decades
many new results from the author have helped
to solve
multiextreme problems arising from important
situations, non-convex
and non linear cases, in function theory.
Foundations of Complex Analysis in Non Locally
Convex Spaces is a
comprehensive book that covers the fundamental
theorems in
Complex and Functional Analysis and presents
much new material.
The book includes generalized new forms of:
Hahn-Banach Theorem,
Multilinear maps, theory of polynomials,
Fixed Point Theorems, p-extreme
points and applications in Operations Research,
Krein-Milman
Theorem, Quasi-differential Calculus, Lagrange
Mean-Value
Theorems, Taylor series, Quasi-holomorphic
and Quasi-analytic
maps, Quasi-Analytic continuations, Fundamental
Theorem of
Calculus, Bolzano's Theorem, Mean-Value Theorem
for Definite
Integral, Bounding and weakly-bounding (limited)
sets,
Holomorphic Completions, and Levi problem.
Each chapter contains illustrative examples
to help the student
and researcher to enhance his knowledge of
theory of functions.
The new concept of Quasi-differentiability
introduced by the
author represents the backbone of the theory
of Holomorphy for
non-locally convex spaces. In fact it is
different but much
stronger than the Frechet one.
The book is intended not only for Post-Graduate
(M.Sc.& Ph.D.)
students and researchers in Complex and Functional
Analysis, but
for all Scientists in various disciplines
whom need nonlinear or
non-convex analysis and holomorphy methods
without convexity
conditions to model and solve problems.
bull; The book contains new generalized versions
of: i)
Fundamental Theorem of Calculus, Lagrange
Mean-Value Theorem in
real and complex cases, Hahn-Banach Theorems,
Bolzano Theorem,
Krein-Milman Theorem, Mean value Theorem
for Definite Integral,
and many others. ii) Fixed Point Theorems
of Bruower, Schauder
and Kakutani's.
bull; The book contains some applications
in Operations research
and non convex analysis as a consequence
of the new concept p-Extreme
points given by the author.
bull; The book contains a complete theory
for Taylor Series
representations of the different types of
holomorphic maps in F-spaces
without convexity conditions.
bull; The book contains a general new concept
of
differentiability stronger than the Frechet
one. This implies a
new Differentiable Calculus called Quasi-differential
(or Bayoumi
differential) Calculus. It is due to the
author's discovery in
1995.
bull; The book contains the theory of polynomials
and Banach
Stienhaus theorem in non convex spaces.
Audience
M.Sc. and Ph.D. students and reseachers in
Analysis, especially
in Complex and Functional Analysis.
Contents
1. Fundamental Theorems in F-Spaces.
2. Theory of Polynomials in F-Spaces.
3. Fixed-Point and P-Extreme Point.
4. Bayoumi (Quasi) Differential Calculus.
5. Generalized Mean-Value Theorem.
6. Higher Quasi-Differential in F-Spaces.
7. Quasi-Holomorphic Maps.
8. New Versions of Main Theorems.
9. Bounding and Weakly-Bounding Sets.
10. Levi Problem in Toplogical Spaces.
Year 2003
Hardbound
ISBN: 0-444-50056-1
278 pages
Studies in Logic and the Foundations of Mathematics,
148
Description
Modal logics, originally conceived in philosophy,
have recently
found many applications in computer science,
artificial
intelligence, the foundations of mathematics,
linguistics and
other disciplines. Celebrated for their good
computational
behaviour, modal logics are used as effective
formalisms for
talking about time, space, knowledge, beliefs,
actions,
obligations, provability, etc. However, the
nice computational
properties can drastically change if we combine
some of these
formalisms into a many-dimensional system,
say, to reason about
knowledge bases developing in time or moving
objects.
To study the computational behaviour of many-dimensional
modal
logics is the main aim of this book. On the
one hand, it is
concerned with providing a solid mathematical
foundation for this
discipline, while on the other hand, it shows
that many seemingly
different applied many-dimensional systems
(e.g., multi-agent
systems, description logics with epistemic,
temporal and dynamic
operators, spatio-temporal logics, etc.)
fit in perfectly with
this theoretical framework, and so their
computational behaviour
can be analyzed using the developed machinery.
We start with concrete examples of applied
one- and many-dimensional
modal logics such as temporal, epistemic,
dynamic, description,
spatial logics, and various combinations
of these. Then we
develop a mathematical theory for handling
a spectrum of
'abstract' combinations of modal logics -
fusions and products of
modal logics, fragments of first-order modal
and temporal logics
- focusing on three major problems: decidability,
axiomatizability, and computational complexity.
Besides the
standard methods of modal logic, the technical
toolkit includes
the method of quasimodels, mosaics, tilings,
reductions to
monadic second-order logic, algebraic logic
techniques. Finally,
we apply the developed machinery and obtained
results to three
case studies from the field of knowledge
representation and
reasoning: temporal epistemic logics for
reasoning about multi-agent
systems, modalized description logics for
dynamic ontologies, and
spatio-temporal logics.
The genre of the book can be defined as a
research monograph. It
brings the reader to the front line of current
research in the
field by showing both recent achievements
and directions of
future investigations (in particular, multiple
open problems). On
the other hand, well-known results from modal
and first-order
logic are formulated without proofs and supplied
with references
to accessible sources.
The intended audience of this book is logicians
as well as those
researchers who use logic in computer science
and artificial
intelligence. More specific application areas
are, e.g.,
knowledge representation and reasoning, in
particular,
terminological, temporal and spatial reasoning,
or reasoning
about agents. And we also believe that researchers
from certain
other disciplines, say, temporal and spatial
databases or
geographical information systems, will benefit
from this book as
well.
Contents
I Introduction
1 Modal logic basics
1.1 Modal axiomatic systems
1.2 Possible world semantics
1.3 Classical first-order logic and the standard
translation
1.4 Multimodal logics
1.5 Algebraic semantics
1.6 Decision, complexity and axiomatizability
problems
2 Applied modal logic
2.1 Temporal logic
2.2 Interval temporal logic
2.3 Epistemic logic
2.4 Dynamic logic
2.5 Description logic
2.6 Spatial logic
2.7 Intuitionistic logic
2.8 'Model level' reductions between logics
3 Many-dimensional modal logics
3.1 Fusions
3.2 Spatio-temporal logics
3.3 Products
3.4 Temporal epistemic logics
3.5 Classical first-order logic as a propositional
multimodal
logic
3.6 First-order modal logics
3.7 First-order temporal logics
3.8 Description logics with modal operators
3.9 HS as a two-dimensional logic
3.10 Modal transition logics
3.11 Intuitionistic modal logics
II Fusions and products
4 Fusions of modal logics
4.1 Preserving Kripke completeness and the
finite model property
4.2 Algebraic preliminaries
4.3 Preserving decidability of global consequence
4.4 Preserving decidability
4.5 Preserving interpolation
4.6 On the computational complexity of fusions
5 Products of modal logics: introduction
5.1 Axiomatizing products
5.2 Proving decidability with quasimodels
5.3 The finite model property
5.4 Proving undecidability
5.5 Proving complexity with tilings
6 Decidable products
6.1 Warming up: Kn x Km
6.2 CPDL x K_m
6.3 Products of epistemic logics with Km
6.4 Products of temporal logics with Km
6.5 Products with S5
6.6 Products with multimodal S5
7 Undecidable products
7.1 Products of linear orders with infinite
ascending chains
7.2 Products of linear orders with infinite
descending chains
7.3 Products of Dedekind complete linear
orders
7.4 Products of finite linear orders
7.5 More undecidable products
8 Higher-dimensional products
8.1 S5 x S5 x ... x S5
8.2 Products between K4 x K4 x ... x K4 and
S5 x S5 x ... x S5
8.3 Products with the fmp
8.4 Between K x K x ... x K and S5 x S5 x
... x S5
8.5 Finitely axiomatizable and decidable
products
9 Variations on products
9.1 Relativized products
9.2 Valuation restrictions
10 Intuitionistic modal logics
10.1 Intuitionistic modal logics with Box
10.2 Intuitionistic modal logics with Box
and Diamond
10.3 The finite model property
III First-order modal logics
11 Fragments of first-order temporal logics
11.1 Undecidable fragments
11.2 Monodic formulas, decidable fragments
11.3 Embedding into monadic second-order
theories
11.4 Complexity of decidable fragments of
QLogSU(N)
11.5 Satisfiability in models over (N,<)
with finite domains
11.6 Satisfiability in models over (R,<)
with finite domains
11.7 Axiomatizing monodic fragments
11.8 Monodicity and equality
12 Fragments of first-order dynamic and epistemic
logics
12.1 Decision problems
12.2 Axiomatizing monodic fragments
IV Applications to knowledge representation
13 Temporal epistemic logics
13.1 Synchronous systems
13.2 Agents who know the time and neither
forget nor learn
14 Modal description logics
14.1 Concept satisfiability
14.2 General formula satisfiability
14.3 Restricted formula satisfiability
14.4 Satisfiability in models with finite
domains
15 Tableaux for modal description logics
15.1 Tableaux for ALC
15.2 Tableaux for K(ALC) with constant domains
15.3 Adding expressive power to K(ALC)
16 Spatio-temporal logics
16.1 Modal formalisms for spatio-temporal
reasoning
16.2 Embedding spatio-temporal logics in
first-order temporal
logic
16.3 Complexity of spatio-temporal logics
16.4 Models based on Euclidean spaces
Epilogue. Bibliography. List of tables. List
of languages and
logics. Symbol index. Subject index.
Year 2003
Hardbound
ISBN: 0-444-50826-0
768 pages