Sergei Kuznetsov is one of the top experts on measure valued branching processes (also known as "superprocesses") and their connection to nonlinear partial differential operators. His research interests range from stochastic processes and partial differential equations to mathematical statistics, time series analysis and statistical software; he has over 90 papers published in international research journals. His most well known contribution to probability theory is the "Kuznetsov-measure." A conference honoring his 60th birthday has been organized at Boulder, Colorado in the summer of 2010, with the participation of Sergei Kuznetsov's mentor and major co-author, Eugene Dynkin. The conference focused on topics related to superprocesses, branching diffusions and nonlinear partial differential equations. In particular, connections to the so-called "Kuznetsov-measure" were emphasized. Leading experts in the field as well as young researchers contributed to the conference. The meeting was organized by J. Englander and B. Rider (U. of Colorado).

These proceedings represent the current state of research on the topics 'boundary theory' and 'spectral and probability theory' of random walks on infinite graphs. They are the result of the two workshops held in Styria (Graz and St. Kathrein am Offenegg, Austria) between June 29th and July 5th, 2009. Many of the participants joined both meetings. Even though the perspectives range from very different fields of mathematics, they all contribute with important results to the same wonderful topic from structure theory, which, by extending a quotation of Laurent Saloff-Coste, could be described by 'exploration of groups by random processes'.

This book explains the foundation of approximate Bayesian computation (ABC), an approach to Bayesian inference that does not require the specification of a likelihood function. As a result, ABC can be used to estimate posterior distributions of parameters for simulation-based models. Simulation-based models are now very popular in cognitive science, as are Bayesian methods for performing parameter inference. As such, the recent developments of likelihood-free techniques are an important advancement for the field. Chapters discuss the philosophy of Bayesian inference as well as provide several algorithms for performing ABC. Chapters also apply some of the algorithms in a tutorial fashion, with one specific application to the Minerva 2 model. In addition, the book discusses several applications of ABC methodology to recent problems in cognitive science. Likelihood-Free Methods for Cognitive Science will be of interest to researchers and graduate students working in experimental, applied, and cognitive science.

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 book deals with methods to evaluate scientific productivity. In the book statistical methods, deterministic and stochastic models and numerous indexes are discussed that will help the reader to understand the nonlinear science dynamics and to be able to develop or construct systems for appropriate evaluation of research productivity and management of research groups and organizations. The dynamics of science structures and systems is complex, and the evaluation of research productivity requires a combination of qualitative and quantitative methods and measures. The book has three parts. The first part is devoted to mathematical models describing the importance of science for economic growth and systems for the evaluation of research organizations of different size. The second part contains descriptions and discussions of numerous indexes for the evaluation of the productivity of researchers and groups of researchers of different size (up to the comparison of research productivities of research communities of nations). Part three contains discussions of non-Gaussian laws connected to scientific productivity and presents various deterministic and stochastic models of science dynamics and research productivity. The book shows that many famous fat tail distributions as well as many deterministic and stochastic models and processes, which are well known from physics, theory of extreme events or population dynamics, occur also in the description of dynamics of scientific systems and in the description of the characteristics of research productivity. This is not a surprise as scientific systems are nonlinear, open and dissipative.

"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.

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.

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 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.

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.

In the theory of random processes the term 'ergodicity' has a wide variety of meanings. In the theory of stationary processes ergodicity is often identified with metric transitivity. In the theory of Markov processes, the word ergodic is applied to theorems of both the existence of transition probability limits and on the convergence of mean value ratios of these transition probabilities. In addition, there are also 'ergodic theorems' on the convergence of distributions of shifted random processes. In this monograph, the term 'ergodic' is understood in its original sense, i.e. the one it had when it was first adopted by the theory of random processes from statistical mechanics and Boltzmann's theory of gases. In this book, an ergodic theorem refers to any statement about the existence of a mean value with respect to trajectories of a random process taken with respect to time. The author takes the view that problems of the existence of time means, and their equality to phase means, are interesting without any assumptions about the distribution of the random process.

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.""

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 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.

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 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.

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.

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.

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 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 introduces data-driven remaining useful life prognosis techniques, and shows how to utilize the condition monitoring data to predict the remaining useful life of stochastic degrading systems and to schedule maintenance and logistics plans. It is also the first book that describes the basic data-driven remaining useful life prognosis theory systematically and in detail. The emphasis of the book is on the stochastic models, methods and applications employed in remaining useful life prognosis. It includes a wealth of degradation monitoring experiment data, practical prognosis methods for remaining useful life in various cases, and a series of applications incorporated into prognostic information in decision-making, such as maintenance-related decisions and ordering spare parts. It also highlights the latest advances in data-driven remaining useful life prognosis techniques, especially in the contexts of adaptive prognosis for linear stochastic degrading systems, nonlinear degradation modeling based prognosis, residual storage life prognosis, and prognostic information-based decision-making.

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.

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.

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.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics," "CFD," "completely integrable systems," "chaos, synergetics and large-scale order," which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.