Bohning; Dankmar
Computer Assisted Analysis of Mixtures and Applications:
Meta Analysis, Disease Mapping, and Others
Description
Beside developments in theory and algorithms, Computer Assisted Analysis of Mixtures and Applications focuses on developments in biometric applications, such as meta-analysis, disease mapping, fertility studies, estimation of prevalence under clustering, and estimation of the distribution of survival time under interval-censoring. The approach is nonparametric for the mixing distribution, including leaving the number of components of the mixing distribution unknown.
Medical andPharmacological Statisticians
Epidemiologists
Social Scientists
Contents
INTRODUCTION
Population Heterogeneity: the Natural Genesis of Mixture Models
Some Examples
Classification Using Posterior Bayes
Parametric or Nonparametric Mixture Models
Connection to Empirical Bayes Estimation
THEORY OF NONPARAMETRIC MIXTURE MODELS
The Likelihood and its Properties
The Directional Derivative and the Gradient Function
The General Mixture Maximum Likelihood Theorem
Applications of the Theorem
ALGORITHMS
Vertex Direction Method
Vertex Exchange Method
Step-Length Choices
C.A. MAN
The EM Algorithm for the Fixed Component Case
THE LIKELIHOOD RATIO TEST FOR THE NUMBER OF COMPONENTS
The Problem
Some Analytical Solutions
Simulation and Bootstrap Solutions
C.A.MAN-APPLICATION: META-ANALYSIS
Conventional Approach
Heterogeneity
C.A.MAN Solution for Modeling Heterogeneity
Classification of Studies Using Posterior Bayes
MOMENT ESTIMATORS OF THE VARIANCE OF MIXING DISTRIBUTION
The DerSimonian-Laird Estimator
The Bohning-Sarol Estimator
Estimation of Binomia- or Poisson Rate Under Heterogeneity
C.A. MAN-APPLICATION: DISEASE MAPPING
Conventional Approach I: Mapping Percentiles
Conventional Approach II: Mapping P-Values
Estimating Map Heterogeneity
OTHER C.A. MAN APPLICATIONS
Fertility Studies
Modeling the Diagnostic Situation
Interval-Censored Survival Data
Features
oSummarizes developments in the area over the last 20 years
Suitable for statisticians involved with clinical trials for the pharmaceutical industry; epidemiologists; and social scientists
ISBN: 1584881798, No of pages: 248
Publication Date: 11/22/99
Gad; Shayne C.
Statistics and Experimental Design for Toxicologists Third Edition
Description
This book serves as a primary text for students of pharmacology, toxicology, and biology, and as a practical handbook to support the daily operations of the toxicology laboratory and researcher. This edition retains the structure of earlier editions, but has been extensively revised to provide both the student and the working toxicologist with the necessary tools for the rigorous and critical design of studies and analysis of experimental data.
Audience
oToxicologists
oPharmacologists
oBiologists
oEpidemiologists
Contents
Introduction
Basic Principles
Experimental Design
Software Programs
Methods for Data Collection, Preparation and Exploration
Hypothesis Testing: Categorical and Ranked Data
Hypothesis Testing: Univariate
Modeling and Extrapolation
Trend Analysis
Methods for Reduction of Dimensionality
Multivariate Methods
Meta Analysis
Data Analysis in Toxicology
Carcinogenesis
Risk Assessment
Epidemiology
Structure Activity Relationships
Frontiers and Controversy
Appendices-Tables
Features
>o Organizes material to provide an ordered development of skills and facilitate ease of access to desired information
Updates material on computational devices
Offers information on SAS software as an aid to solving statistical problems in toxicology
Includes chapters on trend analysis, risk assessment, and epidemiology
Provides a total revision of material on analysis of covariance, with reworked, current examples
Integrates numerous statistical tables, equations, and data into the text to illustrate concepts presented
Statistics and Experimental Design for ToxicologistsThird Edition
ISBN: <1382, No of pages: 448
Publication Date: 08/14/98
Ilegbusi Olusegun Johnson / Northeastern University
Iguchi Manabu / Osaka University
Wahnsiedler Walter E. / Alcoa Technical Center
Mathematical and Physical Modeling of Materials Processing Operations
Description
The past few decades have brought significant advances in the computational methods and in the experimental techniques used to study transport phenomena in materials processing operations. However, the advances have been made independently and with competition between the two approaches. Mathematical models are easier and less costly to implement, but experiments are essential for verifying theoretical models.
In Mathematical and Physical Modeling of Materials Processing Operations, the authors bridge the gap between mathematical modelers and experimentalists. They combine mathematical and physical modeling principles for materials processing operations simulation and use numerous examples to compare theoretical and experimental results.
The modeling of transport processes is multi-disciplinary, involving concepts and principles not all of which can be associated with just one field of study. Therefore, the authors have taken care to ensure that the text is self-sustaining through the variety and breadth of topics covered. Beyond the usual topics associated with transport phenomena, the authors also include detailed discussion of numerical methods and implementation of process models, software and hardware selection and application, and representation of auxiliary relationships, including turbulence modeling, chemical kinetics, magnetohydrodynamics, and multi-phase flow. They also provide several correlations for representing the boundary conditions of fluid flow, heat transfer, and mass transfer phenomena.
Mathematical and Physical Modeling of Materials Processing Operations is ideal for introducing these tools to materials engineers and researchers. Although the book emphasizes material of the topics will prove interesting and useful to researchers in other fields of chemical and mechanical engineering.
Audience
Materials Engineers and Researchers, Chemical Engineers, Mechanical Engineers, Applied Mathematicians, Metallurgists, Manufacturing Engineers.
Contents
INTRODUCTION
Introductory Remarks
Mathematical Modeling
Physical Models
Pilot Plant
BUILDING BLOCKS OF MATHEMATICAL MODELS
Introduction
General Philosophy of Model Development
Some Basic Physical Situations of Relevance to Modeling
SCIENCE BASE OF MATHEMATICAL MODEL DEVELOPMENT
Introduction
Fluid Flow Phenomena
Heat Transfer
Diffusion and Mass Transfer
Multiphase Flow
SUBSIDIARY RELATIONSHIPS USED IN MATHEMATICAL MODELING
Introduction
Chemical Equilibria and Chemical Kinetics
Electromagnetic Flow Phenomena
Non-Newtonian Rheology of Semisolid Slurry Systems
Turbulence Modeling
Useful Correlations
Determination of Physical Properties
SCALING, SCOPING, AND ASYMPTOTIC SOLUTIONS
Introduction
Scaling
Scoping and Asymptotic Solutions
NUMERICAL TECHNIQUES
Introduction
Linear Equations
Nonlinear Equations
Functional Approximation
Numerical Differentiation
Numerical Integration
Ordinary Differential Equations
Partial Differential Equations
Finite Difference Method
Finite Element Method
Orthogonal Collocation
Boundary Integral Method
Optimization
IMPLEMENTATION AND VERIFICATION OF PROCESS MODELS
Introduction
Hardware
Software
Artificial Intelligence
The Future of Modeling Implementations
Verification of Models
MATHEMATICAL MODELING CASE STUDIES
Introduction
Scaling and Scoping-Electrolytic Deposition
Simulations of Fluid Flow and Heat Transfer in Coextrusion
Infiltration Processing of Silicon Carbide
Stoichiometry Driven Marangoni Convection in GaAs Growth
Czochralski Crystal Growth
Flow Characteristics in Gas-Agitated Bath
BASIC ELEMENTS OF PHYSICAL MODELING
Principles of Physical Modeling
Flow Visualization Technique
Measurement of Turbulent Phenomena
Bubble Characteristics
Measurement of Interfacial Phenomena
Measurement of Heat and Mass Transfer
PHYSICAL MODELING EXAMPLES
Bubbling and Jetting
Mixing
Swirl Motion of Bubbling jet
Bubble Characteristics
Liquid Flow Characteristics in a Bath Agitated by Gas Injection
Heat Transfer Between Bubbles and Molten Metal
Heat Transfer Between Solid Body and Molten Metal
Mass Transfer Between Bubbles and Liquid
Mass Transfer Between a Solid Body and Liquid
Entrainment of Top Slag by Lower Molten Metal
Effects of Top Slag on Liquid Flow Characteristics
Turbulence Structure in Bottom Blown Bath with Top Slag Using Conditional Sampling
APPENDICES
Dimensionless Numbers Useful in Process Metallurgy
Fluid Flow Equations in Various Coordinate Systems
Components of the Stress Tensor for Newtonian Fluids in Various Coordinate Systems
The Viscous Dissipation Term for Newtonian Fluids in Various Coordinate Systems
Plus each chapter includes references
Features
A unique, detailed presentation combining into one book both mathematical and physical modeling techniques for materials processing operations
Numerous examples comparing theoretical and experimental results
Strategies for optimal design of materials processing
Topics and applications not usually found in traditional transport phenomena texts and references
Mathematical and Physical Modeling of Materials Processing Operations
ISBN: 1584880171, No of pages: 512
Publication Date: 07/29/99
Leonard; Tom
A Course in Categorical Data Analysis
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 of disciplines.
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
SAMPLING DISTRIBUTIONS
Experimental Design for a Population Proportion
Further Properties of the Binomial Distribution
Statistical Procedures for the Binomial Distribution
The Poisson Distribution
Statistical Procedures for the Poisson Distribution
The Multinomial distribution
Sir Ronald Fisher's Conditioning Result
More General Sampling Models
Generalizing the Binomial Distribution
The Discrete Exponential Family of Distributions
Generalizing the Multinomial Distribution
TWO BY TWO CONTINGENCY TABLES
Conditional Probability and Independence
Independence of Rows and Columns
Investigating Independence, Given Observational Data
Edwards' Theorem
Log Contrasts and the Multinomial Distribution
The Log Measure of Association Test
The Product Binomial Model
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
Testing Equality for two 2 x 2 Tables
The Three-directional Approach of the Analysis 23 Tables
THE MADISON DRUG ALCOHOL ABUSE STUDY
Experimental Design
Statistical Results (phase 3) of Study
Further Validation of Results
GOODMAN'S FULL RANK INTERACTION ANALYZED FOR TWO WAY TABLES
Introductory Example
Methodological Developments
Numerical Example
Methodological Developments
Business School Example
Methodological Developments
Advertising Example
Testing for Equality of Unconditional Cell Probabilities
Analysis of Berkeley Admissions Data
Further Data Sets
FURTHER EXAMPLES AND EXTENSIONS
Hypertension, Obesity, and Alcohol Consumption
The Bristol Cervical Screening Data
The Multiple Sclerosis Data
The Dundee Dental Health Data
CONDITIONAL INDEPENDENCE MODELS FOR TWO-WAY TABLES
Fixed Zeros and Missing Observations
Incomplete Tables
Perfectly Fitting Further Cells
Complete Tables
Further Data Sets
LOGISTIC REGRESSION
Review of General Methodology
Analyzing Your Data Using S-PLUS
Analysis of Mice Exposure Data
Analysis of Space Shuttle Failure Data
Further Data Sets
FURTHER REGRESSION MODELS
Regression Models for Poisson Data
The California Eqrthquake Data
A Generalization of Logistic Regression
Logistic Regression for Matched Case-Control Studies
Further Data
FINAL TOPICS
Continuous Random Variables
Logistic Discrimination Analysis
Testing The Slope and Quadratic Term
Extensions
Three-Way Contingency Tables
INDEX
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
A Course in Categorical Data Analysis
ISBN: 1584881801, No of pages: 208
Publication Date: 11/22/99
Rutter; J W
Geometry of Curves
Description
Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, a need exists for an introduction with modest prerequisites-one that stimulates interest and focuses on problem solving. Integrating the three main areas of curve geometry-parametric, algebraic, and projective curves-Geometry of Curves offers a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. Almost entirely self-contained, this book begins with the basics then takes readers on a fascinating journey from conics, higher algebraic and transcendental curves. It proceeds through the standard properties of parametric curves, the classification of limacons, and an account of
envelopes of curve families, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness.
The uniqueness of this volume lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations.
The result is a practical work that not only imparts a deeper understanding of the theory, but a heightened appreciation of geometry and interest in more advanced studies.
Contents
Preliminaries
Lines, Circles and Conics
Conics: General Position
Some Higher Algebraic and Transcendental Curves
Parameters, Tangents, Normals. Contact, Inflexions
Undulations
Cusps, Non-Regular Points
Curvature
Curvature Applications
Circle of Curvature
Limacons
Evolutes
Parallels, Involutes
Roulettes
Envelopes
Singular Points of Algebraic Curves
Projective Curves
Features
Offers a mathematical framework for problem solving - not just a catalog of theorems
Offers a classification of cubic curves by their singular points - a result typically not available at this level
Includes a section on Watt's curve and the various types of cycloid
Presents numerous examples-accessible, yet giving rise to intriguing complexities
Contains practical exercises that reinforce understanding of theory and pique interest in the subject
Includes MATLAB programs for drawing sized curves
Geometry of Curves
ISBN: 1584881666, No of pages: 384
Publication Date: 02/23/00
Sheskin; David
Handbook of Parametric and Nonparametric Statistical Procedures, Second Edition
Description
Called the "bible of applied" statistics, the first edition of the bestselling Handbook of Parametric and Nonparametric Statistical Procedures was unsurpassed in its scope.
The Second Edition goes even further - more tests, more examples, more than 250 pages of new material.
Thorough - Up-To-Date
With details of more than 100 statistical procedures, the Handbook offers unparalleled coverage of modern statistical methods. You get in-depth discussion of both practical and theoretical issues, many of which are not addressed in conventional statistics books. Practical - User-Friendly
Accessible to novices but valuable to seasoned researchers, the Handbook emphasizes application over theory and presents the procedures in a standardized format that makes it easy to access the information you need.
If you have to
Decide what method of analysis to use
Use a particular test for the first time
Distinguish acceptable from unacceptable research
Interpret the results of published studies
the Handbook of Parametric and Nonparametric Statistical Procedures has the background, the answers, and the guidelines to get the job done.
Audience
Researchers, educators, and students in statistics, psychology, medicine, mathematics, education, and biology, business, and sociology
Contents
Introduction
Outline of Inferential Statistical Tests and Measures of Correlation/Association
Guidelines and Decision Tables for Selecting the Appropriate Statistical Procedure
Inferential Statistical Tests Employed with A Single Sample
Inferential Statistical Tests Employed with Two Independent Samples
Inferential Statistical Tests Employed with Two Dependent Samples
Inferential Statistical Tests Employed with Two or More Independent Samples
Inferential Statistical Tests Employed with Two or More Dependent Samples
Inferential Statistical Test Employed with Factorial Design
Measures of Association/Correlation
Appendix: Tables
Index.
Features
New material added to the second edition
Six chapters on inferential statistical tests - including the single sample test for evaluating population skewness, the single sample test for evaluating population kurtosis,The Kolmogorov-Smirnov goodness-of-fit tests for single and independent samples, and the van der Waerden normal-scores test More detail on the topic of contingency tables - especially the odds ratio- and extensive coverage of meta-analysis
Discussions and examples of data-driven/computer-intensive methods, generation and analysis of random numbers, discrete probability distributions, outliers, data transformation procedures, in-depth coverage of analysis of covariance, and 25 additional tests not included in the first edition, for a total of more than 100 statistical procedures
Handbook of Parametric and Nonparametric Statistical Procedures, Second Edition
ISBN: 158488133X, No of pages: 1016
Publication Date: 02/24/00