"Decision Systems and Non-stochastic Randomness" is the first systematic presentation and mathematical formalization (including existence theorems) of the statistical regularities of non-stochastic randomness. The results presented in this book extend the capabilities of probability theory by providing mathematical techniques that allow for the description of uncertain events that do not fit standard stochastic models. The book demonstrates how non-stochastic regularities can be incorporated into decision theory and information theory, offering an alternative to the subjective probability approach to uncertainty and the unified approach to the measurement of information. This book is intended for statisticians, mathematicians, engineers, economists or other researchers interested in non-stochastic modeling and decision theory.

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.""

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.

This volume presents an eclectic mix of original research articles in areas covering the analysis of ordered data, stochastic modeling and biostatistics. These areas were featured in a conference held at the University of Texas at Dallas from March 7 to 9, 2014 in honor of Professor H. N. Nagaraja's 60th birthday and his distinguished contributions to statistics. The articles were written by leading experts who were invited to contribute to the volume from among the conference participants. The volume is intended for all researchers with an interest in order statistics, distribution theory, analysis of censored data, stochastic modeling, time series analysis, and statistical methods for the health sciences, including statistical genetics.

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.

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.

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.

Features Self-contained book suitable for graduate students and post-doctoral fellows in financial mathematics and data science, as well as for practitioners working in the financial industry who deal with big data All results are presented visually to aid in understanding of concepts.

This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows special case-studies from queueing theory (in particular, the famous problem of Joining the Shorter of Two Queues) and enumerative combinatorics (Counting, Asymptotics). Researchers and graduate students should find this book very useful.

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.

Spatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization. With such versatility, the Voronoi diagram and its relative, the Delaunay triangulation, provide valuable tools for the analysis of spatial data. This is a rapidly growing research area and in this fully updated second edition the authors provide an up-to-date and comprehensive unification of all the previous literature on the subject of Voronoi diagrams. Features:&UL; &LI; Expands on the highly acclaimed first edition&LI; Provides an up-to-date and comprehensive survey of the existing literature on Voronoi diagrams&LI; Includes a useful compendium of applications&LI; Contains an extensive bibliography&/UL; The authors guide the reader through all the necessary mathematical background, before introducing a number of generalizations of Voronoi diagrams in Chapter 3. The subsequent chapters cover algorithms, random Voronoi diagrams, spatial interpolation, multivariate data manipulation, spatial process models, point pattern analysis and locational optimization. Emphasis of a particular perspective is deliberately avoided in order to provide a comprehensive and balanced treatment of the topic. A wide range of applications are discussed, enabling this book to serve as an important reference volume on the topic. The text will appeal to students and researchers studying spatial data in a number of areas, in particular applied probability, computational geometry and Geographic Information Science (GIS). This book will appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both.

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.

Scan statistics is currently one of the most active and important areas of research in applied probability and statistics, having applications to a wide variety of fields: archaeology, astronomy, bioinformatics, biosurveillance, molecular biology, genetics, computer science, electrical engineering, geography, material sciences, physics, reconnaissance, reliability and quality control, telecommunication, and epidemiology. Filling a gap in the literature, this self-contained volume brings together a collection of selected chapters illustrating the depth and diversity of theory, methods and applications in the area of scan statistics.

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."

Written for professionals looking to build data science and analytics capabilities within their organizations as well as those who wish to expand their knowledge and advance their careers in the data space Shows how to build a fit-for-purpose data science capability in a manner that avoids the most common pitfalls Most data strategy works 'top-down' by providing technical solutions to perceived organizational needs. This book uses emergent design, an evolutionary approach that increases the chances of successful outcomes while minimising upfront investment

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.

This book is the third revised and updated English edition of the German textbook \Versuchsplanung und Modellwahl" by Helge Toutenburg which was based on more than 15 years experience of lectures on the course \- sign of Experiments" at the University of Munich and interactions with the statisticians from industries and other areas of applied sciences and en- neering. This is a type of resource/ reference book which contains statistical methods used by researchers in applied areas. Because of the diverse ex- ples combined with software demonstrations it is also useful as a textbook in more advanced courses, The applications of design of experiments have seen a signi?cant growth in the last few decades in di?erent areas like industries, pharmaceutical sciences, medical sciences, engineering sciences etc. The second edition of this book received appreciation from academicians, teachers, students and applied statisticians. As a consequence, Springer-Verlag invited Helge Toutenburg to revise it and he invited Shalabh for the third edition of the book. In our experience with students, statisticians from industries and - searchers from other ?elds of experimental sciences, we realized the importance of several topics in the design of experiments which will - crease the utility of this book. Moreover we experienced that these topics are mostly explained only theoretically in most of the available books.

This book discusses recent developments and the latest research in statistics and its applications, primarily in agriculture and industry, survey sampling and biostatistics, gathering articles on a wide variety of topics. Written by leading academics, scientists, researchers and scholars from around the globe to mark the platinum jubilee of the Department of Statistics, University of Calcutta in 2016, the book is a valuable resource for statisticians, aspiring researchers and professionals across educational levels and disciplines.

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.

Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G."

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.

The term singular spectrum comes from the spectral (eigenvalue) decomposition of a matrix A into its set (spectrum) of eigenvalues. These eigenvalues, A, are the numbers that make the matrix A -AI singular. The term singular spectrum analysis* is unfortunate since the traditional eigenvalue decomposition involving multivariate data is also an analysis of the singular spectrum. More properly, singular spectrum analysis (SSA) should be called the analysis of time series using the singular spectrum. Spectral decomposition of matrices is fundamental to much the ory of linear algebra and it has many applications to problems in the natural and related sciences. Its widespread use as a tool for time series analysis is fairly recent, however, emerging to a large extent from applications of dynamical systems theory (sometimes called chaos theory). SSA was introduced into chaos theory by Fraedrich (1986) and Broomhead and King (l986a). Prior to this, SSA was used in biological oceanography by Colebrook (1978). In the digi tal signal processing community, the approach is also known as the Karhunen-Loeve (K-L) expansion (Pike et aI., 1984). Like other techniques based on spectral decomposition, SSA is attractive in that it holds a promise for a reduction in the dimen- * Singular spectrum analysis is sometimes called singular systems analysis or singular spectrum approach. vii viii Preface sionality. This reduction in dimensionality is often accompanied by a simpler explanation of the underlying physics.

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.