This monograph presents methods for full comparative distributional analysis based on the relative distribution. This provides a general integrated framework for analysis, a graphical component that simplifies exploratory data analysis and display, a statistically valid basis for the development of hypothesis-driven summary measures, and the potential for decomposition - enabling the examination of complex hypotheses regarding the origins of distributional changes within and between groups. Written for data analysts and those interested in measurement, the text can also serve as a textbook for a course on distributional methods.

A critical yet constructive description of the rich analytical techniques and substantive applications that typify how statistical thinking has been applied at the RAND Corporation over the past two decades. Case studies of public policy problems are useful for teaching because they are familiar: almost everyone knows something abut health insurance, global warming, and capital punishment, to name but a few of the applications covered in this casebook. Each case study has a common format that describes the policy questions, the statistical questions, and the successful and the unsuccessful analytic strategies. Readers should be familiar with basic statistical concepts including sampling and regression. While designed for statistics courses in areas ranging from economics to health policy to the law at both the advanced undergraduate and graduate levels, empirical researchers and policy-makers will also find this casebook informative.

The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years - due mainly to the impetus of the authors and their collaborators - a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.

This book introduces the concepts and methods of spatial statistics to geologists and engineers working with oil and gas data, and covers all of the most commonly encountered geostatistical methods for estimation and simulation. Topics include calculation and modeling of semivariograms, linear methods of kriging, cokriging, nonlinear methods such as indicator kriging and disjunctive kriging, and conditional simulation, including sequential indicator simulation, sequential Gaussian simulation, and simulated annealing. Semivariogram models range from very simple to complex. All of the fundamental semivariogram models are illustrated, along with anisotropic models, hole effects, geometric and zonal models, and the mechanics of fitting models. For each geostatistical method treated in detail, the author introduces necessary theory and background, describes how the method works, the steps a user must go through, and problems a user might encounter. The emphasis throughout is on what the practitioner needs to know, and the results that can be expected. The book is replete with examples in two and three dimensions, using real-world data such as porosity and permeability, gas production, structural elevation of a reservoir, and seismic information. Geostatistics and Petroleum Geology will be an invaluable advanced-level text for students on petroleum engineering and geosciences courses, as well as an important reference for petroleum geologists and petroleum engineers in oil companies worldwide.

The book provides a self-contained treatment of stochastic finite element methods. It helps the reader to establish a solid background on stochastic and reliability analysis of structural systems and enables practicing engineers to better manage the concepts of analysis and design in the presence of uncertainty. The book covers the basic topics of computational stochastic mechanics focusing on the stochastic analysis of structural systems in the framework of the finite element method. The target audience primarily comprises students in a postgraduate program specializing in structural engineering but the book may also be beneficial to practicing engineers and research experts alike.

This thesis is devoted to the study of the Bohman-Frieze-Wormald percolation model, which exhibits a discontinuous transition at the critical threshold, while the phase transitions in random networks are originally considered to be robust continuous phase transitions. The underlying mechanism that leads to the discontinuous transition in this model is carefully analyzed and many interesting critical behaviors, including multiple giant components, multiple phase transitions, and unstable giant components are revealed. These findings should also be valuable with regard to applications in other disciplines such as physics, chemistry and biology.

Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of measurement, non-parametric methods result in "ordinal" data. As non-parametric methods make fewer assumptions, their applicability is much wider than the corresponding parametric methods. In particular, they may be applied in situations where less is known about the application in question. Also, due to the reliance on fewer assumptions, non-parametric methods are more robust. Non-parametric methods have many popular applications, and are widely used in research in the fields of the behavioral sciences and biomedicine. This is a textbook on non-parametric statistics for applied research. The authors propose to use a realistic yet mostly fictional situation and series of dialogues to illustrate in detail the statistical processes required to complete data analysis. This book draws on a readers existing elementary knowledge of statistical analyses to broaden his/her research capabilities. The material within the book is covered in such a way that someone with a very limited knowledge of statistics would be able to read and understand the concepts detailed in the text. The "real world" scenario to be presented involves a multidisciplinary team of behavioral, medical, crime analysis, and policy analysis professionals work together to answer specific empirical questions regarding real-world applied problems. The reader is introduced to the team and the data set, and through the course of the text follows the team as they progress through the decision making process of narrowing the data and the research questions to answer the applied problem. In this way, abstract statistical concepts are translated into concrete and specific language. This text uses one data set from which all examples are taken. This is radically different from other statistics books which provide a varied array of examples and data sets. Using only one data set facilitates reader-directed teaching and learning by providing multiple research questions which are integrated rather than using disparate examples and completely unrelated research questions and data.

This volume contains twenty-eight refereed research or review papers presented at the 5th Seminar on Stochastic Processes, Random Fields and Applications, which took place at the Centro Stefano Franscini (Monte Verita) in Ascona, Switzerland, from May 30 to June 3, 2005. The seminar focused mainly on stochastic partial differential equations, random dynamical systems, infinite-dimensional analysis, approximation problems, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance.

A lot of statisticians, actuarial mathematicians, reliability engineers, meteorologists, hydrologists, economists. Business and sport analysts deal with records which play important roles in various fields of statistics and its application. This book enables a reader to check his/her level of understanding of the theory of record values. We give basic formulae which are more important in the theory and present a lot of examples which illustrate the theoretical statements. For a beginner in record statistics, as well as for graduate students the study of our book needs the basic knowledge of the subject. A more advanced reader can use our book to polish his/her knowledge. An upgraded list of bibliography which will help a reader to enrich his/her theoretical knowledge and widen the experience of dealing with ordered observations, is also given in the book.

Since the beginning of the seventies computer hardware is available to use programmable computers for various tasks. During the nineties the hardware has developed from the big main frames to personal workstations. Nowadays it is not only the hardware which is much more powerful, but workstations can do much more work than a main frame, compared to the seventies. In parallel we find a specialization in the software. Languages like COBOL for business orientated programming or Fortran for scientific computing only marked the beginning. The introduction of personal computers in the eighties gave new impulses for even further development, already at the beginning of the seven ties some special languages like SAS or SPSS were available for statisticians. Now that personal computers have become very popular the number of pro grams start to explode. Today we will find a wide variety of programs for almost any statistical purpose (Koch & Haag 1995)."

This monograph is a detailed introductory presentation of the key classes of intelligent data analysis methods. The twelve coherently written chapters by leading experts provide complete coverage of the core issues. The first half of the book is devoted to the discussion of classical statistical issues, ranging from the basic concepts of probability, through general notions of inference, to advanced multivariate and time series methods, as well as a detailed discussion of the increasingly important Bayesian approaches and Support Vector Machines. The following chapters then concentrate on the area of machine learning and artificial intelligence and provide introductions into the topics of rule induction methods, neural networks, fuzzy logic, and stochastic search methods. The book concludes with a chapter on Visualization and a higher-level overview of the IDA processes, which illustrates the breadth of application of the presented ideas.

Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.

The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.

Praise for the Second Edition

"Statistics for Research has other fine qualities besides superior organization. The examples and the statistical methods are laid out with unusual clarity by the simple device of using special formats for each. The book was written with great care and is extremely user-friendly."--The UMAP Journal

Although the goals and procedures of statistical research have changed little since the Second Edition of Statistics for Research was published, the almost universal availability of personal computers and statistical computing application packages have made it possible for today's statisticians to do more in less time than ever before.

The Third Edition of this bestselling text reflects how the changes in the computing environment have transformed the way statistical analyses are performed today. Based on extensive input from university statistics departments throughout the country, the authors have made several important and timely revisions, including: Additional material on probability appears early in the text New sections on odds ratios, ratio and difference estimations, repeated measure analysis, and logistic regression New examples and exercises, many from the field of the health sciences Printouts of computer analyses on all complex procedures An accompanying Web site illustrating how to use SAS(R) and JMP(R) for all procedures

The text features the most commonly used statistical techniques for the analysis of research data. As in the earlier editions, emphasis is placed on how to select the proper statistical procedure and how to interpret results. Whenever possible, to avoid using the computer as a "black box" that performs a mysteriousprocess on the data, actual computational procedures are also given.

A must for scientists who analyze data, professionals and researchers who need a self-teaching text, and graduate students in statistical methods, Statistics for Research, Third Edition brings the methodology up to date in a very practical and accessible way.

S is a high-level language for manipulating, analysing and displaying data. It forms the basis of two highly acclaimed and widely used data analysis software systems, the commercial S-PLUS(R) and the Open Source R. This book provides an in-depth guide to writing software in the S language under either or both of those systems. It is intended for readers who have some acquaintance with S language and want to know how to use it more effectively, for example to build re-usable tools for streamlining routine data analysis or to implement new statistical methods. One ofhe most outstanding strengths of the S language is the ease with which it can be extended by users. S is a functional language, and functions written by users are first-class objects treated in the same way as functions provided by the system. S code is eminently readable and so a good way to document precisely what algorithms were used, and as much of the implementations are themselves written in S, they can be studied as models and to understand their subtleties. The current implementations also provide easy ways for S functions to call compiled code written in C, Fortran and similar languages; this is documented here in depth. Increasingly S is being used for statistical or graphical analysis within larger software systems or for whole vertical-market applications. The interface facilities are most developed on Windows(R) and these are covered with worked examples. The authors have written the widely adopted 'Modern Applied Statistics with S-PLUS', now in its third edition, and several software libraries that enhance S-PLUS and R; these and the examples used in both books are available on the Internet. Dr. W.N. Venables is a senior Statistician with the CSIRO/CMIS Environmentrics Project in Autralia, having been at the Department of Statistics, University of Adelaide for many years previously. Professor B.D. Ripley holds the Chair of Applied Statistics at the University of Oxford, and is the author of four other books on spatial statistics, simulation, pattern recognition and neural networks. Both authors are known and respected thorughout the international S and R communities, for their books, workshops, short courses, freely available software and through their extensive contributions to the S-news and R mailing lists.

Statistical Analysis of Observations of Increasing Dimension is devoted to the investigation of the limit distribution of the empirical generalized variance, covariance matrices, their eigenvalues and solutions of the system of linear algebraic equations with random coefficients, which are an important function of observations in multidimensional statistical analysis. A general statistical analysis is developed in which observed random vectors may not have density and their components have an arbitrary dependence structure. The methods of this theory have very important advantages in comparison with existing methods of statistical processing. The results have applications in nuclear and statistical physics, multivariate statistical analysis in the theory of the stability of solutions of stochastic differential equations, in control theory of linear stochastic systems, in linear stochastic programming, in the theory of experiment planning.

..".the text is user friendly to the topics it considers and should be very accessible...Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."-The Journal of the American Statistical Association

For courses in introductory statistics. Statistics: The Art and Science of Learning from Data takes a conceptual approach, helping students understand what statistics is about and learning the right questions to ask when analysing data, rather than just memorising procedures. This book takes the ideas that have turned statistics into a central science in modern life and makes them accessible, without compromising the necessary rigor. Students will enjoy reading this book, and will stay engaged with its wide variety of real-world data in the examples and exercises. The authors believe that it's important for students to learn and analyse both quantitative and categorical data. As a result, the text pays greater attention to the analysis of proportions than many other introductory statistics texts. Concepts are introduced first with categorical data, and then with quantitative data.

In recent years, there has been an upsurge of interest in using techniques drawn from probability to tackle problems in analysis. These applications arise in subjects such as potential theory, harmonic analysis, singular integrals, and the study of analytic functions. This book presents a modern survey of these methods at the level of a beginning Ph.D. student. Highlights of this book include the construction of the Martin boundary, probabilistic proofs of the boundary Harnack principle, Dahlberg's theorem, a probabilistic proof of Riesz' theorem on the Hilbert transform, and Makarov's theorems on the support of harmonic measure. The author assumes that a reader has some background in basic real analysis, but the book includes proofs of all the results from probability theory and advanced analysis required. Each chapter concludes with exercises ranging from the routine to the difficult. In addition, there are included discussions of open problems and further avenues of research.

This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical understanding of phenomena describing systems in highly inhomogeneous and disordered media, including the KPZ universality class (describing the evolution of interfaces in two dimensions), random walks in random environment and percolative systems. PASI fosters a collaboration between North American and Latin American researchers and students. The conference that inspired this volume took place in January 2012 in both Santiago de Chile and Buenos Aires. Researchers and graduate students will find timely research in probability theory, statistical physics and related disciplines.

This thesis deals with the evaluation of surface and groundwater quality changes in the periods of water scarcity in river catchment areas. The work can be divided into six parts. Existing methods of drought assessment are discussed in the first part, followed by the brief description of the software package HydroOffice, designed by the author. The software is dedicated to analysis of hydrological data (separation of baseflow, parameters of hydrological drought estimation, recession curves analysis, time series analysis). The capabilities of the software are currently used by scientist from more than 30 countries around the world. The third section is devoted to a comprehensive regional assessment of hydrological drought on Slovak rivers, followed by evaluation of the occurrence, course and character of drought in precipitation, discharges, base flow, groundwater head and spring yields in the pilot area of the Nitra River basin. The fifth part is focused on the assessment of changes in surface and groundwater quality during the drought periods within the pilot area. Finally, the results are summarized and interpreted, and rounded off with an outlook to future research.

The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written by a number of specialists on the subject.

The topics selected should give a good overview from the probabilistic and statistical perspective. Included will be articles on fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, and prediction for long-range dependence sequences. For those graduate students and researchers who want to use the methodology and need to know the "tricks of the trade," there will be a special section called "Mathematical Techniques."

Topics in the first part of the book are covered from probabilistic and statistical perspectives and include fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, prediction for long-range dependence sequences. The reader is referred to more detailed proofs if already found in the literature.

The last part of the book is devoted to applications in the areas of simulation, estimation and wavelet techniques, traffic in computer networks, econometry and finance, multifractal models, and hydrology. Diagrams and illustrations enhance the presentation. Each article begins with introductory background material and is accessible to mathematicians, a variety of practitioners, and graduate students. The work serves as a state-of-the art reference or graduate seminar text.

Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website.
The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.