This book contains selected contributions from the geoENV96 - First European Conference on Geostatistics for Environmental Applications, held in Lisbon in November 1996. This is the first of a geoENV series of biennial planned books. The series is intended to show the state of the art of geostatistics in environmental applications with new cases, results and relevant discussions from leading researchers and practitioners around the world. New and important theoretical and practical developments of geostatistics in the environmental field were compiled from three main areas: Hydrology, Groundwater and Groundwater Contamination Soil Contamination and Site Remediation Air Pollution, Ecology and Other Applications The book presents a set of geostatistical tools and approaches used to successfully resolve a variety of specific problems in environment modelling, especially those resulting from the typical scarcity of spatial sampling, the time component of very dynamic systems, the modelling of various systems of contaminants, the uncertainty assessment of health cost functions, etc. Prominent topics concerning methodological tools and methods, stochastic simulation techniques, models of integrating soft information (seismic and remote sensing images), inverse modelling of groundwater flow, neural network classification, change of support and up-scaling are also included in this book. This publication will be of great interest and practical value to geostatisticians working both in universities and in industry.

Often a statistical analysis involves use of a set of alternative models for the data. A "model-selection criterion" is a formula which provides a figure-of merit for the alternative models. Generally the alternative models will involve different numhers of parameters. Model-selection criteria take into account hoth the goodness-or-fit of a model and the numher of parameters used to achieve that fit. 1.1. SETS OF ALTERNATIVE MODELS Thus the focus in this paper is on data-analytic situations ill which there is consideration of a set of alternative models. Choice of a suhset of explanatory variahles in regression, the degree of a polynomial regression, the number of factors in factor analysis, or the numher of dusters in duster analysis are examples of such situations. 1.2. MODEL SELECTION VERSUS HYPOTHESIS TESTING In exploratory data analysis or in a preliminary phase of inference an approach hased on model-selection criteria can offer advantages over tests of hypotheses. The model-selection approach avoids the prohlem of specifying error rates for the tests. With model selection the focus can he on simultaneous competition between a hroad dass of competing models rather than on consideration of a sequence of simpler and simpler models."

The approach of layer-damping coordinate transformations to treat singularly perturbed equations is a relatively new, and fast growing area in the field of applied mathematics. This monograph aims to present a clear, concise, and easily understandable description of the qualitative properties of solutions to singularly perturbed problems as well as of the essential elements, methods and codes of the technology adjusted to numerical solutions of equations with singularities by applying layer-damping coordinate transformations and corresponding layer-resolving grids. The first part of the book deals with an analytical study of estimates of the solutions and their derivatives in layers of singularities as well as suitable techniques for obtaining results. In the second part, a technique for building the coordinate transformations eliminating boundary and interior layers, is presented. Numerical algorithms based on the technique which is developed for generating layer-damping coordinate transformations and their corresponding layer-resolving meshes are presented in the final part of this volume. This book will be of value and interest to researchers in computational and applied mathematics.

This is a new, completely revised, updated and enlarged edition of the author's Ergebnisse vol. 46: "Spin Glasses: A Challenge for Mathematicians" in two volumes (this is the 2nd volume). In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses." These models are simple and rather canonical random structures, of considerable interest for several branches of science (statistical physics, neural networks and computer science). The physicists studied them by non-rigorous methods and predicted spectacular behaviors. This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics. The present Volume II contains a considerable amount of new material, in particular all the fundamental low-temperature results obtained after the publication of the first edition.

The author investigates athermal fluctuation from the viewpoints of statistical mechanics in this thesis. Stochastic methods are theoretically very powerful in describing fluctuation of thermodynamic quantities in small systems on the level of a single trajectory and have been recently developed on the basis of stochastic thermodynamics. This thesis proposes, for the first time, a systematic framework to describe athermal fluctuation, developing stochastic thermodynamics for non-Gaussian processes, while thermal fluctuations are mainly addressed from the viewpoint of Gaussian stochastic processes in most of the conventional studies. First, the book provides an elementary introduction to the stochastic processes and stochastic thermodynamics. The author derives a Langevin-like equation with non-Gaussian noise as a minimal stochastic model for athermal systems, and its analytical solution by developing systematic expansions is shown as the main result. Furthermore, the a uthor shows a thermodynamic framework for such non-Gaussian fluctuations, and studies some thermodynamics phenomena, i.e. heat conduction and energy pumping, which shows distinct characteristics from conventional thermodynamics. The theory introduced in the book would be a systematic foundation to describe dynamics of athermal fluctuation quantitatively and to analyze their thermodynamic properties on the basis of stochastic methods.

This book covers the basic statistical and analytical techniques of computer intrusion detection. It is aimed at both statisticians looking to become involved in the data analysis aspects of computer security and computer scientists looking to expand their toolbox of techniques for detecting intruders. The book is self-contained, assumng no expertise in either computer security or statistics. It begins with a description of the basics of TCP/IP, followed by chapters dealing with network traffic analysis, network monitoring for intrusion detection, host based intrusion detection, and computer viruses and other malicious code. Each section develops the necessary tools as needed. There is an extensive discussion of visualization as it relates to network data and intrusion detection. The book also contains a large bibliography covering the statistical, machine learning, and pattern recognition literature related to network monitoring and intrusion detection. David Marchette is a scientist at the Naval Surface Warfacre Center in Dalhgren, Virginia. He has worked at Navy labs for 15 years, doing research in pattern recognition, computational statistics, and image analysis. He has been a fellow by courtesy in the mathematical sciences department of the Johns Hopkins University since 2000. He has been working in conputer intrusion detection for several years, focusing on statistical methods for anomaly detection and visualization. Dr. Marchette received a Masters in Mathematics from the University of California, San Diego in 1982 and a Ph.D. in Computational Sciences and Informatics from George Mason University in 1996.

Gian-Carlo Rota was born in Vigevano, Italy, in 1932. He died in Cambridge, Mas sachusetts, in 1999. He had several careers, most notably as a mathematician, but also as a philosopher and a consultant to the United States government. His mathe matical career was equally varied. His early mathematical studies were at Princeton (1950 to 1953) and Yale (1953 to 1956). In 1956, he completed his doctoral thesis under the direction of Jacob T. Schwartz. This thesis was published as the pa per "Extension theory of differential operators I", the first paper reprinted in this volume. Rota's early work was in analysis, more specifically, in operator theory, differ ential equations, ergodic theory, and probability theory. In the 1960's, Rota was motivated by problems in fluctuation theory to study some operator identities of Glen Baxter (see [7]). Together with other problems in probability theory, this led Rota to study combinatorics. His series of papers, "On the foundations of combi natorial theory", led to a fundamental re-evaluation of the subject. Later, in the 1990's, Rota returned to some of the problems in analysis and probability theory which motivated his work in combinatorics. This was his intention all along, and his early death robbed mathematics of his unique perspective on linkages between the discrete and the continuous. Glimpses of his new research programs can be found in [2,3,6,9,10].

This book offers a comprehensive guide to the modelling of operational risk using possibility theory. It provides a set of methods for measuring operational risks under a certain degree of vagueness and impreciseness, as encountered in real-life data. It shows how possibility theory and indeterminate uncertainty-encompassing degrees of belief can be applied in analysing the risk function, and describes the parametric g-and-h distribution associated with extreme value theory as an interesting candidate in this regard. The book offers a complete assessment of fuzzy methods for determining both value at risk (VaR) and subjective value at risk (SVaR), together with a stability estimation of VaR and SVaR. Based on the simulation studies and case studies reported on here, the possibilistic quantification of risk performs consistently better than the probabilistic model. Risk is evaluated by integrating two fuzzy techniques: the fuzzy analytic hierarchy process and the fuzzy extension of techniques for order preference by similarity to the ideal solution. Because of its specialized content, it is primarily intended for postgraduates and researchers with a basic knowledge of algebra and calculus, and can be used as reference guide for research-level courses on fuzzy sets, possibility theory and mathematical finance. The book also offers a useful source of information for banking and finance professionals investigating different risk-related aspects.

These three volumes comprise the proceedings of the US/Japan Conference, held in honour of Professor H. Akaike, on the Frontiers of Statistical Modeling: an Informational Approach'. The major theme of the conference was the implementation of statistical modeling through an informational approach to complex, real-world problems. Volume 1 contains papers which deal with the Theory and Methodology of Time Series Analysis. Volume 1 also contains the text of the Banquet talk by E. Parzen and the keynote lecture of H. Akaike. Volume 2 is devoted to the general topic of Multivariate Statistical Modeling, and Volume 3 contains the papers relating to Engineering and Scientific Applications. For all scientists whose work involves statistics.

This book is unique in covering a wide range of design and analysis issues in genetic studies of rare variants, taking advantage of collaboration of the editors with many experts in the field through large-scale international consortia including the UK10K Project, GO-T2D and T2D-GENES. Chapters provide details of state-of-the-art methodology for rare variant detection and calling, imputation and analysis in samples of unrelated individuals and families. The book also covers analytical issues associated with the study of rare variants, such as the impact of fine-scale population structure, and with combining information on rare variants across studies in a meta-analysis framework. Genetic association studies have in the last few years substantially enhanced our understanding of factors underlying traits of high medical importance, such as body mass index, lipid levels, blood pressure and many others. There is growing empirical evidence that low-frequency and rare variants play an important role in complex human phenotypes. This book covers multiple aspects of study design, analysis and interpretation for complex trait studies focusing on rare sequence variation. In many areas of genomic research, including complex trait association studies, technology is in danger of outstripping our capacity to analyse and interpret the vast amounts of data generated. The field of statistical genetics in the whole-genome sequencing era is still in its infancy, but powerful methods to analyse the aggregation of low-frequency and rare variants are now starting to emerge. The chapter Functional Annotation of Rare Genetic Variants is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

A unique, practical guide for industry professionals who need to improve product quality and reliability in repairable systems

Owing to its vital role in product quality, reliability has been intensely studied in recent decades. Most of this research, however, addresses systems that are nonrepairable and therefore discarded upon failure. Statistical Methods for the Reliability of Repairable Systems fills the gap in the field, focusing exclusively on an important yet long-neglected area of reliability. Written by two highly recognized members of the reliability and statistics community, this new work offers a unique, systematic treatment of probabilistic models used for repairable systems as well as the statistical methods for analyzing data generated from them.

Liberally supplemented with examples as well as exercises boasting real data, the book clearly explains the difference between repairable and nonrepairable systems and helps readers develop an understanding of stochastic point processes. Data analysis methods are discussed for both single and multiple systems and include graphical methods, point estimation, interval estimation, hypothesis tests, goodness-of-fit tests, and reliability prediction. Complete with extensive graphs, tables, and references, Statistical Methods for the Reliability of Repairable Systems is an excellent working resource for industry professionals involved in producing reliable systems and a handy reference for practitioners and researchers in the field.

Spatial statistics are useful in subjects as diverse as climatology, ecology, economics, environmental and earth sciences, epidemiology, image analysis and more. This book covers the best-known spatial models for three types of spatial data: geostatistical data (stationarity, intrinsic models, variograms, spatial regression and space-time models), areal data (Gibbs-Markov fields and spatial auto-regression) and point pattern data (Poisson, Cox, Gibbs and Markov point processes). The level is relatively advanced, and the presentation concise but complete.

The most important statistical methods and their asymptotic properties are described, including estimation in geostatistics, autocorrelation and second-order statistics, maximum likelihood methods, approximate inference using the pseudo-likelihood or Monte-Carlo simulations, statistics for point processes and Bayesian hierarchical models. A chapter is devoted to Markov Chain Monte Carlo simulation (Gibbs sampler, Metropolis-Hastings algorithms and exact simulation).
A large number of real examples are studied with R, and each chapter ends with a set of theoretical and applied exercises. While a foundation in probability and mathematical statistics is assumed, three appendices introduce some necessary background. The book is accessible to senior undergraduate students with a solid math background and Ph.D. students in statistics. Furthermore, experienced statisticians and researchers in the above-mentioned fields will find the book valuable as a mathematically sound reference.

This book is the English translation of Modelisation et Statistique Spatiales published by Springer in the series Mathematiques & Applications, a series established by Societe de Mathematiques Appliquees et Industrielles (SMAI)."

This book discusses dynamical systems that are typically driven by stochastic dynamic noise. It is written by two statisticians essentially for the statistically inclined readers, although readers whose primary interests are in determinate systems will find some of the methodology explained in this book of interest. The statistical approach adopted in this book differs in many ways from the deterministic approach to dynamical systems. Even the very basic notion of initial-value sensitivity requires careful development in the new setting provided. This book covers, in varying depth, many of the contributions made by the statisticians in the past twenty years or so towards our understanding of estimation, the Lyapunov-like index, the nonparametric regression, and many others, many of which are motivated by their dynamical system counterparts but have now acquired a distinct statistical flavour. Kung-Sik Chan is a professor at the University of Iowa, Department of Statistics and Actuarial Science. He is an elected member of the International Statistical Institute. He has served on the editorial boards of the Journal of Business and Economic Statistics and Statistica Sinica. He received a Faculty Scholar Award from the University of Iowa in 1996. Howell Tong holds the Chair of Statistics at the London School of Economics and the University of Hong Kong. He is a foreign member of the Norwegian Academy of Science and Letters, an elected member of the International Statistical Institute and a Council member of its Bernoulli Society, an elected fellow of the Institute of Mathematical Statistics, and an honorary fellow of the Institute of Actuaries (London). He was the Founding Dean of the Graduate School and sometimes the Acting Pro-Vice Chancellor (Research) at the University of Hong Kong. He has served on the editorial boards of several international journals, including Biometrika, Journal of Royal Statistical Society (Series B), Statistica Sinica, and others. He is a guest professor of the Academy of Mathematical and System Sciences of the Chinese Academy of Sciences and received a National Natural Science Prize (China) in the category of Mathematics and Mechanics (Class II) in 2001. He has also held visiting professorships at various universities, including the Imperial College in London, the ETH in Zurich, the Fourier University in Grenoble, the Wall Institute at the University of British Columbia, Vancouver, and the Chinese University of Hong Kong.

Multivariate polynomials are a main tool in approximation. The book begins with an introduction to the general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book gives the first comprehensive introduction to the recently developped theory of generalized hyperinterpolation. As an application, the book gives a quick introduction to tomography. Several parts of the book are based on rotation principles, which are presented in the beginning of the book, together with all other basic facts needed.

This volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics. Each paper represents a contribution by Prof. McKean, either alone or together with other researchers, that has had a profound influence in the respective area.

The domain of non-extensive thermostatistics has been subject to intensive research over the past twenty years and has matured significantly. Generalised Thermostatistics cuts through the traditionalism of many statistical physics texts by offering a fresh perspective and seeking to remove elements of doubt and confusion surrounding the area. The book is divided into two parts - the first covering topics from conventional statistical physics, whilst adopting the perspective that statistical physics is statistics applied to physics. The second developing the formalism of non-extensive thermostatistics, of which the central role is played by the notion of a deformed exponential family of probability distributions. Presented in a clear, consistent, and deductive manner, the book focuses on theory, part of which is developed by the author himself, but also provides a number of references towards application-based texts. Written by a leading contributor in the field, this book will provide a useful tool for learning about recent developments in generalized versions of statistical mechanics and thermodynamics, especially with respect to self-study. Written for researchers in theoretical physics, mathematics and statistical mechanics, as well as graduates of physics, mathematics or engineering. A prerequisite knowledge of elementary notions of statistical physics and a substantial mathematical background are required.

Edexcel and A Level Modular Mathematics S2 features: Student-friendly worked examples and solutions, leading up to a wealth of practice questions. Sample exam papers for thorough exam preparation. Regular review sections consolidate learning. Opportunities for stretch and challenge presented throughout the course. 'Escalator section' to step up from GCSE. PLUS Free LiveText CD-ROM, containing Solutionbank and Exam Cafe to support, motivate and inspire students to reach their potential for exam success. Solutionbank contains fully worked solutions with hints and tips for every question in the Student Books. Exam Cafe includes a revision planner and checklist as well as a fully worked examination-style paper with examiner commentary.

Learn how to apply the principles of machine learning to time series modeling with this indispensable resource Machine Learning for Time Series Forecasting with Python is an incisive and straightforward examination of one of the most crucial elements of decision-making in finance, marketing, education, and healthcare: time series modeling. Despite the centrality of time series forecasting, few business analysts are familiar with the power or utility of applying machine learning to time series modeling. Author Francesca Lazzeri, a distinguished machine learning scientist and economist, corrects that deficiency by providing readers with comprehensive and approachable explanation and treatment of the application of machine learning to time series forecasting. Written for readers who have little to no experience in time series forecasting or machine learning, the book comprehensively covers all the topics necessary to: Understand time series forecasting concepts, such as stationarity, horizon, trend, and seasonality Prepare time series data for modeling Evaluate time series forecasting models' performance and accuracy Understand when to use neural networks instead of traditional time series models in time series forecasting Machine Learning for Time Series Forecasting with Python is full real-world examples, resources and concrete strategies to help readers explore and transform data and develop usable, practical time series forecasts. Perfect for entry-level data scientists, business analysts, developers, and researchers, this book is an invaluable and indispensable guide to the fundamental and advanced concepts of machine learning applied to time series modeling.

This volume presents original research contributed to the 3rd Annual International Conference on Computational Mathematics and Computational Geometry (CMCGS 2014), organized and administered by Global Science and Technology Forum (GSTF). Computational Mathematics and Computational Geometry are closely related subjects, but are often studied by separate communities and published in different venues. This volume is unique in its combination of these topics. After the conference, which took place in Singapore, selected contributions chosen for this volume and peer-reviewed. The section on Computational Mathematics contains papers that are concerned with developing new and efficient numerical algorithms for mathematical sciences or scientific computing. They also cover analysis of such algorithms to assess accuracy and reliability. The parts of this project that are related to Computational Geometry aim to develop effective and efficient algorithms for geometrical applications such as representation and computation of surfaces. Other sections in the volume cover Pure Mathematics and Statistics ranging from partial differential equations to matrix analysis, finite difference or finite element methods and function approximation. This volume will appeal to advanced students and researchers in these areas.

Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately.

This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations.

Several researchers, colleagues, friends and students of Professor Maria Luisa Menendez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work."

This volume presents selections of Peter J. Bickel's major papers, along with comments on their novelty and impact on the subsequent development of statistics as a discipline. Each of the eight parts concerns a particular area of research and provides new commentary by experts in the area. The parts range from Rank-Based Nonparametrics to Function Estimation and Bootstrap Resampling. Peter's amazing career encompasses the majority of statistical developments in the last half-century or about about half of the entire history of the systematic development of statistics. This volume shares insights on these exciting statistical developments with future generations of statisticians. The compilation of supporting material about Peter's life and work help readers understand the environment under which his research was conducted. The material will also inspire readers in their own research-based pursuits. This volume includes new photos of Peter Bickel, his biography, publication list, and a list of his students. These give the reader a more complete picture of Peter Bickel as a teacher, a friend, a colleague, and a family man.

"The outstanding strengths of the book are its topic coverage, references, exposition, examples and problem sets... This book is an excellent addition to any mathematical statistician's library." -Bulletin of the American Mathematical Society In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.

This work supplies the reader with formulas, maps out the procedure to follow, and provides working charts, tables, and calculating machines to allow the reader to compute statistics for application to problems in psychology and education.

The aim of this book is to report on the progress realized in probability theory in the field of dynamic random walks and to present applications in computer science, mathematical physics and finance. Each chapter contains didactical material as well as more advanced technical sections. Few appendices will help refreshing memories (if necessary!).
. New probabilistic model, new results in probability theory
. Original applications in computer science
. Applications in mathematical physics
. Applications in finance