This volume contains the Proceedings of the Advanced Symposium on Multivariate Modeling and Data Analysis held at the 64th Annual Heeting of the Virginia Academy of Sciences (VAS)--American Statistical Association's Vir ginia Chapter at James Madison University in Harrisonburg. Virginia during Hay 15-16. 1986. This symposium was sponsored by financial support from the Center for Advanced Studies at the University of Virginia to promote new and modern information-theoretic statist ical modeling procedures and to blend these new techniques within the classical theory. Multivariate statistical analysis has come a long way and currently it is in an evolutionary stage in the era of high-speed computation and computer technology. The Advanced Symposium was the first to address the new innovative approaches in multi variate analysis to develop modern analytical and yet practical procedures to meet the needs of researchers and the societal need of statistics. vii viii PREFACE Papers presented at the Symposium by e1l11lJinent researchers in the field were geared not Just for specialists in statistics, but an attempt has been made to achieve a well balanced and uniform coverage of different areas in multi variate modeling and data analysis. The areas covered included topics in the analysis of repeated measurements, cluster analysis, discriminant analysis, canonical cor relations, distribution theory and testing, bivariate densi ty estimation, factor analysis, principle component analysis, multidimensional scaling, multivariate linear models, nonparametric regression, etc."

This book presents a large variety of extensions of the methods of inclusion and exclusion. Both methods for generating and methods for proof of such inequalities are discussed. The inequalities are utilized for finding asymptotic values and for limit theorems. Applications vary from classical probability estimates to modern extreme value theory and combinatorial counting to random subset selection. Applications are given in prime number theory, growth of digits in different algorithms, and in statistics such as estimates of confidence levels of simultaneous interval estimation. The prerequisites include the basic concepts of probability theory and familiarity with combinatorial arguments.

This timely and synoptic text contains the essentials of queueing networks, from the classical product-form theory to the more recent developments such as diffusion and fluid limits, stochastic comparisons, stability, dynamic scheduling, and optimization. Written by two leading experts in stochastic models and applied probability, the book is based on the authors' lecture notes accumulated over many years of teaching queueing networks. The selection of materials is well-balanced in breadth and depth, making the book an ideal graduate-level text for students in engineering, business, applied mathematics, and probability and statistics. As queueing networks have become widely used as a basic model of many physical systems in a diverse range of fields, from supply chains to communication networks, the book is also a useful reference for researchers and practitioners in industrial engineering, operations research and management, computer systems, telecommunications, and related fields.

During the past decade interest in quality management has greatly increased. One of the central elements of Total Quality Management is Statistical Process Control, more commonly known as SPC. This book describes the pitfalls and traps which businesses encounter when implementing and assuring SPC. Illustrations are given from practical experience in various companies. The following subjects are discussed: implementation of SPC, activity plan for achieving statistically controlled processes, statistical tools, and lastly, consolidation and improvement of the results. Also, an extensive checklist is provided with which a business can determine to what extent it has succeeded in the actual application of SPC. Audience: This volume is written for companies which are going to implement SPC, or which need a new impetus in order to get SPC properly off the ground. It will be of interest in particular to researchers whose work involves statistics and probability, production, operation and manufacturing management, industrial organisation and mathematical and quantitative methods. It will also appeal to specialists in engineering and management, for example in the electronic industry, discrete parts industry, process industry, automotive and aircraft industry and food industry.

The Handbook is written for academics, researchers, practitioners and advanced graduate students. It has been designed to be read by those new or starting out in the field of spatial analysis as well as by those who are already familiar with the field. The chapters have been written in such a way that readers who are new to the field will gain important overview and insight. At the same time, those readers who are already practitioners in the field will gain through the advanced and/or updated tools and new materials and state-of-the-art developments included. This volume provides an accounting of the diversity of current and emergent approaches, not available elsewhere despite the many excellent journals and te- books that exist. Most of the chapters are original, some few are reprints from the Journal of Geographical Systems, Geographical Analysis, The Review of Regional Studies and Letters of Spatial and Resource Sciences. We let our contributors - velop, from their particular perspective and insights, their own strategies for m- ping the part of terrain for which they were responsible. As the chapters were submitted, we became the first consumers of the project we had initiated. We gained from depth, breadth and distinctiveness of our contributors' insights and, in particular, the presence of links between them.

The editors draw on a 3-year project that analyzed a Portuguese area in detail, comparing this study with papers from other regions. Applications include the estimation of technical efficiency in agricultural grazing systems (dairy, beef and mixed) and specifically for dairy farms. The conclusions indicate that it is now necessary to help small dairy farms in order to make them more efficient. These results can be compared with the technical efficiency of a sample of Spanish dairy processing firms presented by Magdalena Kapelko and co-authors.

In recent years, the theory has become widely accepted and has been further developed, but a detailed introduction is needed in order to make the material available and accessible to a wide audience. This will be the first book providing such an introduction, covering core theory and recent developments which can be applied to many application areas. All authors of individual chapters are leading researchers on the specific topics, assuring high quality and up-to-date contents. An Introduction to Imprecise Probabilities provides a comprehensive introduction to imprecise probabilities, including theory and applications reflecting the current state if the art. Each chapter is written by experts on the respective topics, including: Sets of desirable gambles; Coherent lower (conditional) previsions; Special cases and links to literature; Decision making; Graphical models; Classification; Reliability and risk assessment; Statistical inference; Structural judgments; Aspects of implementation (including elicitation and computation); Models in finance; Game- theoretic probability; Stochastic processes (including Markov chains); Engineering applications. Essential reading for researchers in academia, research institutes and other organizations, as well as practitioners engaged in areas such as risk analysis and engineering.

This book employs a computable general equilibrium (CGE) model - a widely used economic model which uses actual data to provide economic analysis and policy assessment - and applies it to economic data on Singapore's tourism industry. The authors set out to demonstrate how a novice modeller can acquire the necessary skills and knowledge to successfully apply general equilibrium models to tourism studies. The chapters explain how to build a computable general equilibrium model for tourism, how to conduct simulation and, most importantly, how to analyse modelling results. This applied study acts as a modelling book at both introductory and intermediate levels, specifically targeting students and researchers who are interested in and wish to learn computable general equilibrium modelling. The authors offer insightful analysis of Singapore's tourism industry and provide both students and researchers with a guide on how to apply general equilibrium models to actual economic data and draw accurate conclusions.

The last decade has seen a remarkable development of the "Marginal and Moment Problems" as a research area in Probability and Statistics. Its attractiveness stemmed from its lasting ability to provide a researcher with difficult theoretical problems that have direct consequences for appli cations outside of mathematics. The relevant research aims centered mainly along the following lines that very frequently met each other to provide sur prizing and useful results: -To construct a probability distribution (to prove its existence, at least) with a given support and with some additional inner stochastic property defined typically either by moments or by marginal distributions. -To study the geometrical and topological structure of the set of prob ability distributions generated by such a property mostly with the aim to propose a procedure that would result in a stochastic model with some optimal properties within the set of probability distributions. These research aims characterize also, though only very generally, the scientific program of the 1996 conference "Distributions with given marginals and moment problems" held at the beginning of September in Prague, Czech Republic, to perpetuate the tradition and achievements of the closely related 1990 Roma symposium "On Frechet Classes" 1 and 1993 Seattle" AMS Summer Conference on Marginal Problem.""

The book develops the capabilities arising from the cooperation between mathematicians and statisticians working in insurance and finance fields. It gathers some of the papers presented at the conference MAF2010, held in Ravello (Amalfi coast), and successively, after a reviewing process, worked out to this aim.

This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.

This monograph is intended for scientists and TCAD engineers who are interested in physics-based simulation of Si and SiGe devices. The common theoretical background of the drift-diffusion, hydrodynamic, and Monte-Carlo models and their synergy are discussed and it is shown how these models form a consistent hierarchy of simulation tools. The basis of this hierarchy is the full-band Monte-Carlo device model which is discussed in detail, including its numerical and stochastic properties. The drift-diffusion and hydrodynamic models for large-signal, small-signal, and noise analysis are derived from the Boltzmann transport equation in such a way that all transport and noise parameters can be obtained by Monte-Carlo simulations. With this hierarchy of simulation tools the device characteristics of strained Si MOSFETs and SiGe HBTs are analysed and the accuracy of the momentum-based models is assessed by comparison with the Monte-Carlo device simulator.

This guide is for practicing statisticians and data scientists who use IBM SPSS for statistical analysis of big data in business and finance. This is the first of a two-part guide to SPSS for Windows, introducing data entry into SPSS, along with elementary statistical and graphical methods for summarizing and presenting data. Part I also covers the rudiments of hypothesis testing and business forecasting while Part II will present multivariate statistical methods, more advanced forecasting methods, and multivariate methods. IBM SPSS Statistics offers a powerful set of statistical and information analysis systems that run on a wide variety of personal computers. The software is built around routines that have been developed, tested, and widely used for more than 20 years. As such, IBM SPSS Statistics is extensively used in industry, commerce, banking, local and national governments, and education. Just a small subset of users of the package include the major clearing banks, the BBC, British Gas, British Airways, British Telecom, the Consumer Association, Eurotunnel, GSK, TfL, the NHS, Shell, Unilever, and W.H.S. Although the emphasis in this guide is on applications of IBM SPSS Statistics, there is a need for users to be aware of the statistical assumptions and rationales underpinning correct and meaningful application of the techniques available in the package; therefore, such assumptions are discussed, and methods of assessing their validity are described. Also presented is the logic underlying the computation of the more commonly used test statistics in the area of hypothesis testing. Mathematical background is kept to a minimum.

Study smarter and stay on top of your probability course with the bestselling Schaum's Outline-now with the NEW Schaum's app and website! Schaum's Outline of Probability, Third Edition is the go-to study guide for help in probability courses. It's ideal for undergrads, graduate students and professionals needing a tool for review. With an outline format that facilitates quick and easy review and mirrors the course in scope and sequence, this book helps you understand basic concepts and get the extra practice you need to excel in the course. Schaum's Outline of Probability, Third Edition supports the bestselling textbooks and is useful for a variety of classes, including Elementary Probability and Statistics, Data Analysis, Finite Mathematics, and many other courses. You'll find coverage on finite and countable sets, binomial coefficients, axioms of probability, conditional probability, expectation of a finite random variable, Poisson distribution, and probability of vectors and Stochastic matrices. Also included: finite Stochastic and tree diagrams, Chebyshev's inequality and the law of large numbers, calculations of binomial probabilities using normal approximation, and regular Markov processes and stationary state distributions. Features *NEW to this edition: the new Schaum's app and website! *NEW to this edition: 20 NEW problem-solving videos online *430 solved problems *Outline format to provide a concise guide to the standard college course in probability *Clear, concise explanations of probability concepts *Supports these major texts: Elementary Statistics: A Step by Step Approach (Bluman), Mathematics with Applications (Hungerford), and Discrete Mathematics and Its Applications (Rosen) *Appropriate for the following courses: Elementary Probability and Statistics, Data Analysis, Finite Mathematics, Introduction to Mathematical Statistics, Mathematics for Biological Sciences, Introductory Statistics, Discrete Mathematics, Probability for Applied Science, and Introduction to Probability Theory

Sample Sizes for Clinical Trials, Second Edition is a practical book that assists researchers in their estimation of the sample size for clinical trials. Throughout the book there are detailed worked examples to illustrate both how to do the calculations and how to present them to colleagues or in protocols. The book also highlights some of the pitfalls in calculations as well as the key steps that lead to the final sample size calculation. Features: Comprehensive coverage of sample size calculations, including Normal, binary, ordinal, and survival outcome data Covers superiority, equivalence, non-inferiority, bioequivalence and precision objectives for both parallel group and crossover designs Highlights how trial objectives impact the study design with respect to both the derivation of sample formulae and the size of the study Motivated with examples of real-life clinical trials showing how the calculations can be applied New edition is extended with all chapters revised, some substantially, and four completely new chapters on multiplicity, cluster trials, pilot studies, and single arm trials The book is primarily aimed at researchers and practitioners of clinical trials and biostatistics, and could be used to teach a course on sample size calculations. The importance of a sample size calculation when designing a clinical trial is highlighted in the book. It enables readers to quickly find an appropriate sample size formula, with an associated worked example, complemented by tables to assist in the calculations.

Continuous-time Markov decision processes (MDPs), also known as controlled Markov chains, are used for modeling decision-making problems that arise in operations research (for instance, inventory, manufacturing, and queueing systems), computer science, communications engineering, control of populations (such as fisheries and epidemics), and management science, among many other fields. This volume provides a unified, systematic, self-contained presentation of recent developments on the theory and applications of continuous-time MDPs. The MDPs in this volume include most of the cases that arise in applications, because they allow unbounded transition and reward/cost rates. Much of the material appears for the first time in book form.

Conditional Monte Carlo: Gradient Estimation and Optimization Applications deals with various gradient estimation techniques of perturbation analysis based on the use of conditional expectation. The primary setting is discrete-event stochastic simulation. This book presents applications to queueing and inventory, and to other diverse areas such as financial derivatives, pricing and statistical quality control. To researchers already in the area, this book offers a unified perspective and adequately summarizes the state of the art. To researchers new to the area, this book offers a more systematic and accessible means of understanding the techniques without having to scour through the immense literature and learn a new set of notation with each paper. To practitioners, this book provides a number of diverse application areas that makes the intuition accessible without having to fully commit to understanding all the theoretical niceties. In sum, the objectives of this monograph are two-fold: to bring together many of the interesting developments in perturbation analysis based on conditioning under a more unified framework, and to illustrate the diversity of applications to which these techniques can be applied. Conditional Monte Carlo: Gradient Estimation and Optimization Applications is suitable as a secondary text for graduate level courses on stochastic simulations, and as a reference for researchers and practitioners in industry.

This book explains a procedure for constructing realistic stochastic differential equation models for randomly varying systems in biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation.

This book presents the state of the art of biostatistical methods and their applications in clinical oncology. Many methodologies established today in biostatistics have been brought about through its applications to the design and analysis of oncology clinical studies. This field of oncology, now in the midst of evolution owing to rapid advances in biotechnologies and cancer genomics, is becoming one of the most promising disease fields in the shift toward personalized medicine. Modern developments of diagnosis and therapeutics of cancer have also been continuously fueled by recent progress in establishing the infrastructure for conducting more complex, large-scale clinical trials and observational studies. The field of cancer clinical studies therefore will continue to provide many new statistical challenges that warrant further progress in the methodology and practice of biostatistics. This book provides a systematic coverage of various stages of cancer clinical studies. Topics from modern cancer clinical trials include phase I clinical trials for combination therapies, exploratory phase II trials with multiple endpoints/treatments, and confirmative biomarker-based phase III trials with interim monitoring and adaptation. It also covers important areas of cancer screening, prognostic analysis, and the analysis of large-scale molecular data in the era of big data.

Knowledge acquisition is one of the most important aspects influencing the quality of methods used in artificial intelligence and the reliability of expert systems. The various issues dealt with in this volume concern many different approaches to the handling of partial knowledge and to the ensuing methods for reasoning and decision making under uncertainty, as applied to problems in artificial intelligence. The volume is composed of the invited and contributed papers presented at the Workshop on Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, held at the Ettore Majorana Center for Scientific Culture of Erice (Sicily, Italy) on June 19-25, 1994, in the framework of the International School of Mathematics "G.Stampacchia." It includes also a transcription of the roundtable held during the workshop to promote discussions on fundamental issues, since in the choice of invited speakers we have tried to maintain a balance between the various schools of knowl edge and uncertainty modeling. Choquet expected utility models are discussed in the paper by Alain Chateauneuf: they allow the separation of perception of uncertainty or risk from the valuation of outcomes, and can be of help in decision mak ing. Petr Hajek shows that reasoning in fuzzy logic may be put on a strict logical (formal) basis, so contributing to our understanding of what fuzzy logic is and what one is doing when applying fuzzy reasoning."

This book moves systematically through the topic of applied probability from an introductory chapter to such topics as random variables and vectors, stochastic processes, estimation, testing and regression. The topics are well chosen and the presentation is enriched by many examples from real life. Each chapter concludes with many original, solved and unsolved problems and hundreds of multiple choice questions, enabling those unfamiliar with the topics to master them. Additionally appealing are historical notes on the mathematicians mentioned throughout, and a useful bibliography. A distinguishing character of the book is its thorough and succinct handling of the varied topics.

A balanced presentation of both theoretical and applied material with numerous problem sets to illustrate important concepts. Demonstrates the use of computers and calculators to facilitate problem solving, as well as numerous applications to illustrate basic theory.

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

The present text introduces the student to the basic ideas of estimation and hypothesis testing early in the course after a rather brief introduction to data organization and some simple ideas about probability. Estimation and hypothesis testing are discussed in terms of the two-sample problem. The book exploits nonparametric ideas that rely on nothing more complicated than sample differences Y-X, referred to as elementary estimates, to define the Wilcoxon-Mann-Whitney test statistics and the related point and interval estimates. The ideas behind elementary estimates are then applied to the one-sample problem and to linear regression and rank correlation. Discussion of the Kruskal-Wallis and Friedman procedures for the k-sample problem rounds out the nonparametric coverage. The concluding chapters provide a discussion of Chi-square tests for the analysis of categorical data and introduce the student to the analysis of binomial data including the computation of power and sample size. Most chapters in the book have an appendix discussing relevant Minitab commands.

Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theory and development of numerical algorithms. Building on students' skills in calculus and linear algebra, the text provides a rigorous exposition without undue abstraction. Its stress on statistical applications will be especially appealing to graduate students of statistics and biostatistics. The intended audience also includes students in applied mathematics, computational biology, computer science, economics, and physics who want to see rigorous mathematics combined with real applications. In this second edition the emphasis remains on finite-dimensional optimization. New material has been added on the MM algorithm, block descent and ascent, and the calculus of variations. Convex calculus is now treated in much greater depth. Advanced topics such as the Fenchel conjugate, subdifferentials, duality, feasibility, alternating projections, projected gradient methods, exact penalty methods, and Bregman iteration will equip students with the essentials for understanding modern data mining techniques in high dimensions.