Geostatistics for Engineers and Earth Scientists

The four volumes of Game Equilibrium Models present applications of non-cooperative game theory. Problems of strategic interaction arising in biology, economics, political science and the social sciences in general are treated in 42 papers on a wide variety of subjects. Internationally known authors with backgrounds in various disciplines have contributed original research. The reader finds innovative modelling combined with advanced methods of analysis. The four volumes are the outcome of a research year at the Center for Interdisciplinary Studies of the University of Bielefeld. The close interaction of an international interdisciplinary group of researchers has produced an unusual collection of remarkable results of great interest for everybody who wants to be informed on the scope, potential, and future direction of work in applied game theory. Volume IV Social and Political Interaction contains game equilibrium models focussing on social and political interaction within communities or states or between states, i.e. national and international social and political interaction. Specific aspects of those interactions are modelled as non-cooperative games and their equilibria are analysed.

This monograph provides a careful review of the major statistical techniques used to analyze regression data with nonconstant variability and skewness. The authors have developed statistical techniques--such as formal fitting methods and less formal graphical techniques-- that can be applied to many problems across a range of disciplines, including pharmacokinetics, econometrics, biochemical assays, and fisheries research.

While the main focus of the book in on data transformation and weighting, it also draws upon ideas from diverse fields such as influence diagnostics, robustness, bootstrapping, nonparametric data smoothing, quasi-likelihood methods, errors-in-variables, and random coefficients. The authors discuss the computation of estimates and give numerous examples using real data. The book also includes an extensive treatment of estimating variance functions in regression.

Stochastic Processes: General Theory starts with the fundamental existence theorem of Kolmogorov, together with several of its extensions to stochastic processes. It treats the function theoretical aspects of processes and includes an extended account of martingales and their generalizations. Various compositions of (quasi- or semi-)martingales and their integrals are given. Here the Bochner boundedness principle plays a unifying role: a unique feature of the book. Applications to higher order stochastic differential equations and their special features are presented in detail. Stochastic processes in a manifold and multiparameter stochastic analysis are also discussed. Each of the seven chapters includes complements, exercises and extensive references: many avenues of research are suggested. The book is a completely revised and enlarged version of the author's Stochastic Processes and Integration (Noordhoff, 1979). The new title reflects the content and generality of the extensive amount of new material. Audience: Suitable as a text/reference for second year graduate classes and seminars. A knowledge of real analysis, including Lebesgue integration, is a prerequisite.

This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces.
Key Features:
- Complete state of the art of the importance of triangular norms in various mathematical fields
- 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications
- Chapter authors are leading authorities in their fields
- Triangular norms on different domains (including discrete, partially ordered) are described
- Not only triangular norms but also related operators (aggregation operators, copulas) are covered
- Book contains many enlightening illustrations
- Complete state of the art of the importance of triangular norms in various mathematical fields
- 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications
- Chapter authors are leading authorities in their fields
- Triangular norms on different domains (including discrete, partially ordered) are described
- Not only triangular norms but also related operators (aggregation operators, copulas) are covered
- Book contains many enlightening illustrations

This volume contains 20 refereed research or review papers presented at the five-day Third Seminar on Stochastic Analysis, Random Fields and Applications which took place at the Centro Stefano Franscini (Monte Verit ) in Ascona, Switzerland, from September 20 to 24, 1999. The seminar focused on three topics: fundamental aspects of stochastic analysis, physical modeling, and applications to financial engineering. The third topic was the subject of a mini-symposium on stochastic methods in financial models.

Features: Second edition has been updated with a new chapter on Nonparametric Estimation; a significant update to the chapter on Statistical Decision Theory; and other updates throughout No requirement for heavy calculus, and simple questions throughout the text help students check their understanding of the material Each chapter also includes a set of exercises that range in level of difficulty Self-contained, and can be used by the students to understand the theory Chapters and sections marked by asterisks contain more advanced topics and may be omitted Special chapters on linear models and nonparametric statistics show how the main theoretical concepts can be applied to well-known and frequently used statistical tools

This books reviews and brings readers up to date with the latest research knowledge on road traffic safety. It describes and discusses mathematical descriptions of the process of a motor vehicle crash and indicates the various factors that impact on collision models. It tackles also vehicle stability and shows how the forces generated in crashes result in different extents of post-accident repair. Mathematical models that simulate vehicle stability data are compared with those of real vehicles. Practical uses of the models are explained to readers. The book will be of interest to researchers in transport and vehicle technology well as automotive industry professionals.

This timely text presents a comprehensive guide to genetic association, a new and rapidly expanding field that aims to elucidate how our genetic code (genotypes) influences the traits we possess (phenotypes). The book provides a detailed review of methods of gene mapping used in association with experimental crosses, as well as genome-wide association studies. Emphasis is placed on model selection procedures for analyzing data from large-scale genome scans based on specifically designed modifications of the Bayesian information criterion. Features: presents a thorough introduction to the theoretical background to studies of genetic association (both genetic and statistical); reviews the latest advances in the field; illustrates the properties of methods for mapping quantitative trait loci using computer simulations and the analysis of real data; discusses open challenges; includes an extensive statistical appendix as a reference for those who are not totally familiar with the fundamentals of statistics.

The four volumes of Game Equilibrium Models present applications of non-cooperative game theory. Problems of strategic interaction arising in biology, economics, political science and the social sciences in general are treated in 42 papers on a wide variety of subjects. Internationally known authors with backgrounds in various disciplines have contributed original research. The reader finds innovative modelling combined with advanced methods of analysis. The four volumes are the outcome of a research year at the Center for Interdisciplinary Studies of the University of Bielefeld. The close interaction of an international interdisciplinary group of researchers has produced an unusual collection of remarkable results of great interest for everybody who wants to be informed on the scope, potential, and future direction of work in applied game theory. Volume III Strategic Bargaining contains ten papers on game equilibrium models of bargaining. All these contributions look at bargaining situations as non-cooperative games. General models of two-person and n-person bargaining are explored.

This pioneering work deals with the parameterization of rockfalls in the context of 3D run-out modelling at a study site in the Bavarian Alps. The main objective was to cover not only low-magnitude, high-frequency rockfalls (<10 m3) but also Mid-Magnitude events, which involve rock volumes of between 10 and 100 m3 (boulder falls) and between 100 and 10,000 m3 (block falls). As Mid-Magnitude events have been insufficiently covered in terms of rockfall modelling up to now, a geomechanical approach has been developed to characterize those events by means of a case study. For a 200 m3 limestone block a potential failure scenario was analysed by combining a deterministic failure analysis with a numerical process-based run-out model. To model potential run-out scenarios of the 200 m3 block, the beta version of the code RAMMS::Rockfall, developed by the Swiss Institute for Snow and Avalanche Research (SLF), was applied. RAMMS::Rockfall makes it possible to include the block shape and thus consider the effects of varying block shapes on the run-out distance. The run-out modelling for the entire project site was performed using the scientific code Rockyfor3D (Dorren/ecorisQ). To provide quantitative information in terms of input parameters, a field recording of block sizes at the talus slope, as well as a detailed discontinuity analysis at the source area, were conducted. The book successfully demonstrates how detailed and quantitative field investigation can contribute to 3D rockfall modelling.

This book is designed as a textbook for graduate students and as a resource for researchers seeking a thorough mathematical treatment of its subject. It develops the main results of regression and the analysis of variance, as well as the central results on confounded and fractional factorial experiments. Matrix theory is deemphasized; its role is taken instead by the theory of linear transformations between vector spaces.The text gives a carefully paced and unified presentation of two topics, linear models and experimental design. Students are assumed to have a solid background in linear algebra, basic knowledge of regression and analysis of variance, and some exposure to experimental design, and should be comfortable with reading and constructing mathematical proofs. The book leads students into the mathematical theory, including many examples both for motivation and for illustration. Over 130 exercises of varying difficulty are included. An extensive mathematical appendix and a detailed index make the text especially accessible. Linear Models and Design can serve as a textbook for a year-long course in the topics covered, or for a one-semester course in either linear model theory or experimental design. It prepares students for more advanced topics in the field, and assists in developing a thoughtful approach to the existing literature. It includes a guide to terminology as well as discussion of the history and development of ideas, and offers a fresh perspective on the fundamental concepts and results of the subject.

In recent years portfolio optimization and construction methodologies have become an increasingly critical ingredient of asset and fund management, while at the same time portfolio risk assessment has become an essential ingredient in risk management, and this trend will only accelerate in the coming years. Unfortunately there is a large gap between the limited treatment of portfolio construction methods that are presented in most university courses with relatively little hands-on experience and limited computing tools, and the rich and varied aspects of portfolio construction that are used in practice in the finance industry. Current practice demands the use of modern methods of portfolio construction that go well beyond the classical Markowitz mean-variance optimality theory and require the use of powerful scalable numerical optimization methods. This book fills the gap between current university instruction and current industry practice by providing a comprehensive computationally-oriented treatment of modern portfolio optimization and construction methods. The computational aspect of the book is based on extensive use of S-PlusA(R), the S+NuOPTa"[ optimization module, the S-Plus Robust Library and the S]Bayesa"[ Library, along with about 100 S-Plus scripts and some CRSPA(R) sample data sets of stock returns. A special time-limited version of the S-Plus software is available to purchasers of this book.

a oeFor money managers and investment professionals in the field, optimization is truly a can of worms rather left un-opened, until now! Here lies a thorough explanation of almost all possibilities one can think of for portfolio optimization, complete with error estimationtechniques and explanation of when non-normality plays a part. A highly recommended and practical handbook for the consummate professional and student alike!a

Steven P. Greiner, Ph.D., Chief Large Cap Quant & Fundamental Research Manager, Harris Investment Management

a oeThe authors take a huge step in the long struggle to establish applied post-modern portfolio theory. The optimization and statistical techniques generalize the normal linear model to include robustness, non-normality, and semi-conjugate Bayesian analysis via MCMC. The techniques are very clearly demonstrated by the extensive use and tight integration of S-Plus software. Their book should be an enormous help to students and practitioners trying to move beyond traditional modern portfolio theory.a

Peter Knez, CIO, Global Head of Fixed Income, Barclays Global Investors

a oeWith regard to static portfolio optimization, the book gives a good survey on the development from the basic Markowitz approach to state of the art models and is in particular valuable for direct use in practice or for lectures combined with practical exercises.a

Short Book Reviews of the International Statistical Institute, December 2005

The book presents important tools and techniques for treating problems in m- ern multivariate statistics in a systematic way. The ambition is to indicate new directions as well as to present the classical part of multivariate statistical analysis in this framework. The book has been written for graduate students and statis- cians who are not afraid of matrix formalism. The goal is to provide them with a powerful toolkit for their research and to give necessary background and deeper knowledge for further studies in di?erent areas of multivariate statistics. It can also be useful for researchers in applied mathematics and for people working on data analysis and data mining who can ?nd useful methods and ideas for solving their problems. Ithasbeendesignedasatextbookforatwosemestergraduatecourseonmultiva- ate statistics. Such a course has been held at the Swedish Agricultural University in 2001/02. On the other hand, it can be used as material for series of shorter courses. In fact, Chapters 1 and 2 have been used for a graduate course "Matrices in Statistics" at University of Tartu for the last few years, and Chapters 2 and 3 formed the material for the graduate course "Multivariate Asymptotic Statistics" in spring 2002. An advanced course "Multivariate Linear Models" may be based on Chapter 4. A lot of literature is available on multivariate statistical analysis written for di?- ent purposes and for people with di?erent interests, background and knowledge.

This book provides an overview of the role of statistics in Risk Analysis, by addressing theory, methodology and applications covering the broad scope of risk assessment in life sciences and public health, environmental science as well as in economics and finance. Experimental Design plays a key role in many of these areas, therefore there is special attention paid to joining Risk Analysis and Experimental Design topics. The contributions of this volume originate from the 8th International Conference on Risk Analysis (23-26 April, 2019, Vienna). The conference brought together researchers and practitioners working in the field of Risk Analysis. The most important contributions at the conference have been refereed and developed into chapters to show the latest developments in the field.

Waiting in lines is a staple of everyday human life. Without really noticing, we are doing it when we go to buy a ticket at a movie theater, stop at a bank to make an account withdrawal, or proceed to checkout a purchase from one of our favorite department stores. Oftentimes, waiting lines are due to overcrowded, overfilling, or congestion; any time there is more customer demand for a service than can be provided, a waiting line forms. Queuing systems is a term used to describe the methods and techniques most ideal for measuring the probability and statistics of a wide variety of waiting line models. This book provides an introduction to basic queuing systems, such as M/M/1 and its variants, as well as newer concepts like systems with priorities, networks of queues, and general service policies. Numerical examples are presented to guide readers into thinking about practical real-world applications, and students and researchers will be able to apply the methods learned to designing queuing systems that extend beyond the classroom. Very little has been published in the area of queuing systems, and this volume will appeal to graduate-level students, researchers, and practitioners in the areas of management science, applied mathematics, engineering, computer science, and statistics.

This textbook introduces the mathematical concepts and methods that underlie statistics. The course is unified, in the sense that no prior knowledge of probability theory is assumed; this is developed as needed. The book is committed to a high level of mathematical seriousness; and to an intimate connection with application. Modern methods, such as logistic regression, are introduced; as are unjustly neglected clasical topics, such as elementary asymptotics.
The book first develops elementary linear models for measured data and multiplicative models for counted data. Simple probability models for random error follow. The most important famiies of random variables are then studied in detail, emphasizing their interrelationships and their large-sample behavior. Inference, including classical, Bayesian, finite population, and likelihood-based, is introduced as the necessary mathematical tools become available.
In teaching style, the book aims to be
* mathematically complete: every formula is derived, every theorem proved at the appropriate level
* concrete: each new concept is introduced and exemplified by interesting statistical problems; and more abstract concepts appear only gradually
* constructive: direct derivations and proofs are preferred
* active: students are led to do mathematical statistics, not just to appreciate it, with the assistance of 500 interesting exercises.
The text is aimed for the upper undergraduate level, or the beginning Masters program level. It assumes the usual two-year college mathematics sequence, including an introduction to multiple integrals, matrix algebra, and infinite series.
George R. Terrell received his degrees from Rice University, where he later taught. Since 1986 he has taught in the Statistics Department of Virginia Polytechnic Institute and State University.

This paper represents the collaborative work of a game theorist and a policy analyst in an attempt to examine severa! questions that go to the hearl of the way individuala achieve social order. The capacity of any individual to undertake long-term, productive activities that affect and are affected by the actiona of other individuala dependa upon gaining a minimallevel of predictability among those involved. No one could successfully drive to work if the behavior of other drivera were noi relatively predictable. No one could operate a stare, if potential consumers did not purcha. se, rather than stea!, the commodities offered to the public. No one would ma. ke a. ny investments other than those tha. t would be made by a solitary individual in an isolated setting (the cla. ssic Robinson Crusoe situation). One of the ways that individuals achieve predictability in social arrangements is to a. gree to follow a set of normative prescriptions a. bout what they must, must not, or may do. Agreeing to a set of prescriptions is relatively easy. Actually following those prescriptions over time when temptations arise offering potentially high payoffs, is not at all easy. In natural settings, individUala follow agreed upon prescriptions to a greater or lesser extent depending on enforcement levels. A frequent assumption made by policy ana. lysts a. nd game theorists is tha. t enforcement is externa! to the situa. tion under analysis. That a.

Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given to the technique's practical value. Furthermore, the subject has been rather inaccessible to the general statistician.

The account presented in this book places emphasis on topics of methodological importance, in the hope that this will facilitate broader practical application of density estimation and also encourage research into relevant theoretical work. The book also provides an introduction to the subject for those with general interests in statistics. The important role of density estimation as a graphical technique is reflected by the inclusion of more than 50 graphs and figures throughout the text.

Several contexts in which density estimation can be used are discussed, including the exploration and presentation of data, nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, bump hunting, projection pursuit, and the estimation of hazard rates and other quantities that depend on the density. This book includes general survey of methods available for density estimation. The Kernel method, both for univariate and multivariate data, is discussed in detail, with particular emphasis on ways of deciding how much to smooth and on computation aspects. Attention is also given to adaptive methods, which smooth to a greater degree in the tails of the distribution, and to methods based on the idea of penalized likelihood.

This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data. This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods for solving linear systems will be introduced for finding the stationary distribution of a Markov chain. The chapter then covers the basic theories and algorithms for hidden Markov models (HMMs) and Markov decision processes (MDPs). Chapter 2 discusses the applications of continuous time Markov chains to model queueing systems and discrete time Markov chain for computing the PageRank, the ranking of websites on the Internet. Chapter 3 studies Markovian models for manufacturing and re-manufacturing systems and presents closed form solutions and fast numerical algorithms for solving the captured systems. In Chapter 4, the authors present a simple hidden Markov model (HMM) with fast numerical algorithms for estimating the model parameters. An application of the HMM for customer classification is also presented. Chapter 5 discusses Markov decision processes for customer lifetime values. Customer Lifetime Values (CLV) is an important concept and quantity in marketing management. The authors present an approach based on Markov decision processes for the calculation of CLV using real data. Chapter 6 considers higher-order Markov chain models, particularly a class of parsimonious higher-order Markov chain models. Efficient estimation methods for model parameters based on linear programming are presented. Contemporary research results on applications to demand predictions, inventory control and financial risk measurement are also presented. In Chapter 7, a class of parsimonious multivariate Markov models is introduced. Again, efficient estimation methods based on linear programming are presented. Applications to demand predictions, inventory control policy and modeling credit ratings data are discussed. Finally, Chapter 8 re-visits hidden Markov models, and the authors present a new class of hidden Markov models with efficient algorithms for estimating the model parameters. Applications to modeling interest rates, credit ratings and default data are discussed. This book is aimed at senior undergraduate students, postgraduate students, professionals, practitioners, and researchers in applied mathematics, computational science, operational research, management science and finance, who are interested in the formulation and computation of queueing networks, Markov chain models and related topics. Readers are expected to have some basic knowledge of probability theory, Markov processes and matrix theory.

In the third and final book of his iconic piano etudes Gyoergy Ligeti charts a new path relative to the rest of his musical output, representing a significant arrival in a composer's oeuvre known for its stylistic transformations. This monograph is the first dedicated study of these capstone works, investigating them through a novel lens of statistical-graphical analysis that illuminates their compositional uniqueness as well as broader questions regarding the perception of stability in musical texture. With nearly 200 graphical illustrations and a detailed commentary, this examination reveals the unique manner in which Ligeti treads between tonality and atonality-a key idea in his late style-and the centrality of processes related to broader scale areas (or "macroharmony") in articulating structures and narratives. The analytical techniques developed here are a powerful tool for investigating macroharmonic stability that can be applied to a wide range of repertoire beyond these works. This book is intended for graduate-level and professional music theorists, musicologists, performers and mathematicians.

This book is designed as a supplement to an introductory undergraduate or graduate course for mathematics, science and engineering students of all disciplines. the text covers all major aspects of engineering statistics, including descriptive statistics, probability and probability distributions, statistical test and confidence intervals for one and two samples and curve fitting, correlation, regression, chi-square tests, and analysis of variance. The book continues to maintain a student-friendly approach and numerical problem solving orientation. Presentations are limited to very basic topics to serve as an introduction to advance topics in those areas of discipline. The purpose of the book is to present the principles and concepts of Probability and Statistics as relevant to student learning.