Weather derivatives are financial instruments that can be used by organizations or individuals as part of a risk management strategy to minimize risk associated with adverse or unexpected weather conditions. Just as traditional contingent claims, a weather derivative has an underlying measure, such as: rainfall, wind, snow or temperature. Nearly $1 trillion of the U.S. economy is directly exposed to weather-related risk. More precisely, almost 30% of the U.S. economy and 70% of U.S. companies are affected by weather. The purpose of this monograph is to conduct an in-depth analysis of financial products that are traded in the weather market. Presenting a pricing and modeling approach for weather derivatives written on various underlying weather variables will help students, researchers, and industry professionals accurately price weather derivatives, and will provide strategies for effectively hedging against weather-related risk. This book will link the mathematical aspects of the modeling procedure of weather variables to the financial markets and the pricing of weather derivatives. Very little has been published in the area of weather risk, and this volume will appeal to graduate-level students and researchers studying financial mathematics, risk management, or energy finance, in addition to investors and professionals within the financial services industry. "

Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area. The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts. The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.

This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition. This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications. Reviews of First Edition: "This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology." (Siam Review, Vol. 45 (2), 2003) "This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences." (Short Book Reviews of the ISI, Vol. 23 (2), 2003)

Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.

Nature didn't design human beings to be statisticians, and in fact our minds are more naturally attuned to spotting the saber-toothed tiger than seeing the jungle he springs from. Yet scienti?c discovery in practice is often more jungle than tiger. Those of us who devote our scienti?c lives to the deep and satisfying subject of statistical inference usually do so in the face of a certain under-appreciation from the public, and also (though less so these days) from the wider scienti?c world. With this in mind, it feels very nice to be over-appreciated for a while, even at the expense of weathering a 70th birthday. (Are we certain that some terrible chronological error hasn't been made?) Carl Morris and Rob Tibshirani, the two colleagues I've worked most closely with, both 't my ideal pro?le of the statistician as a mathematical scientist working seamlessly across wide areas of theory and application. They seem to have chosen the papers here in the same catholic spirit, and then cajoled an all-star cast of statistical savants to comment on them.

This book covers the method of metric distances and its application in probability theory and other fields. The method is fundamental in the study of limit theorems and generally in assessing the quality of approximations to a given probabilistic model. The method of metric distances is developed to study stability problems and reduces to the selection of an ideal or the most appropriate metric for the problem under consideration and a comparison of probability metrics. After describing the basic structure of probability metrics and providing an analysis of the topologies in the space of probability measures generated by different types of probability metrics, the authors study stability problems by providing a characterization of the ideal metrics for a given problem and investigating the main relationships between different types of probability metrics. The presentation is provided in a general form, although specific cases are considered as they arise in the process of finding supplementary bounds or in applications to important special cases. Svetlozar T. Rachev is the Frey Family Foundation Chair of Quantitative Finance, Department of Applied Mathematics and Statistics, SUNY-Stony Brook and Chief Scientist of Finanlytica, USA. Lev B. Klebanov is a Professor in the Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic. Stoyan V. Stoyanov is a Professor at EDHEC Business School and Head of Research, EDHEC-Risk Institute-Asia (Singapore). Frank J. Fabozzi is a Professor at EDHEC Business School. (USA)

The primary purpose of this textbook is to introduce the reader to a wide variety of elementary permutation statistical methods. Permutation methods are optimal for small data sets and non-random samples, and are free of distributional assumptions. The book follows the conventional structure of most introductory books on statistical methods, and features chapters on central tendency and variability, one-sample tests, two-sample tests, matched-pairs tests, one-way fully-randomized analysis of variance, one-way randomized-blocks analysis of variance, simple regression and correlation, and the analysis of contingency tables. In addition, it introduces and describes a comparatively new permutation-based, chance-corrected measure of effect size. Because permutation tests and measures are distribution-free, do not assume normality, and do not rely on squared deviations among sample values, they are currently being applied in a wide variety of disciplines. This book presents permutation alternatives to existing classical statistics, and is intended as a textbook for undergraduate statistics courses or graduate courses in the natural, social, and physical sciences, while assuming only an elementary grasp of statistics.

This book deals with the application of wavelet and spectral methods for the analysis of nonlinear and dynamic processes in economics and finance. It reflects some of the latest developments in the area of wavelet methods applied to economics and finance. The topics include business cycle analysis, asset prices, financial econometrics, and forecasting. An introductory paper by James Ramsey, providing a personal retrospective of a decade's research on wavelet analysis, offers an excellent overview over the field.

Limit theorems and asymptotic results form a central topic in probability theory and mathematical statistics. New and non-classical limit theorems have been discovered for processes in random environments, especially in connection with random matrix theory and free probability. These questions and the techniques for answering them combine asymptotic enumerative combinatorics, particle systems and approximation theory, and are important for new approaches in geometric and metric number theory as well. Thus, the contributions in this book include a wide range of applications with surprising connections ranging from longest common subsequences for words, permutation groups, random matrices and free probability to entropy problems and metric number theory.

The book is the product of a conference that took place in August 2011 in Bielefeld, Germany to celebrate the 60th birthday of Friedrich Gotze, a noted expert in this field."

This book presents a step by step Asset Health Management Optimization Approach Using Internet of Things (IoT). The authors provide a comprehensive study which includes the descriptive, diagnostic, predictive, and prescriptive analysis in detail. The presentation focuses on the challenges of the parameter selection, statistical data analysis, predictive algorithms, big data storage and selection, data pattern recognition, machine learning techniques, asset failure distribution estimation, reliability and availability enhancement, condition based maintenance policy, failure detection, data driven optimization algorithm, and a multi-objective optimization approach, all of which can significantly enhance the reliability and availability of the system.

Nonparametric function estimation with stochastic data, otherwise known as smoothing, has been studied by several generations of statisticians. Assisted by the ample computing power in today's servers, desktops, and laptops, smoothing methods have been finding their ways into everyday data analysis by practitioners. While scores of methods have proved successful for univariate smoothing, ones practical in multivariate settings number far less. Smoothing spline ANOVA models are a versatile family of smoothing methods derived through roughness penalties, that are suitable for both univariate and multivariate problems. In this book, the author presents a treatise on penalty smoothing under a unified framework. Methods are developed for (i) regression with Gaussian and non-Gaussian responses as well as with censored lifetime data; (ii) density and conditional density estimation under a variety of sampling schemes; and (iii) hazard rate estimation with censored life time data and covariates. The unifying themes are the general penalized likelihood method and the construction of multivariate models with built-in ANOVA decompositions. Extensive discussions are devoted to model construction, smoothing parameter selection, computation, and asymptotic convergence. Most of the computational and data analytical tools discussed in the book are implemented in R, an open-source platform for statistical computing and graphics. Suites of functions are embodied in the R package gss, and are illustrated throughout the book using simulated and real data examples. This monograph will be useful as a reference work for researchers in theoretical and applied statistics as well as for those in other related disciplines. It can also be used as a text for graduate level courses on the subject. Most of the materials are accessible to a second year graduate student with a good training in calculus and linear algebra and working knowledge in basic statistical inferences such as linear models and maximum likelihood estimates.

In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 "Mathematical Methods for Extracting Quantifiable Information from Complex Systems." This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.

Researchers and students who use empirical investigation in their work must go through the process of selecting statistical methods for analyses, and they are often challenged to justify these selections. This book is designed for readers with limited background in statistical methodology who seek guidance in defending their statistical decision-making in the worlds of research and practice. It is devoted to helping students and scholars find the information they need to select data analytic methods, and to speak knowledgeably about their statistical research processes. Each chapter opens with a conundrum relating to the selection of an analysis, or to explaining the nature of an analysis. Throughout the chapter, the analysis is described, along with some guidance in justifying the choices of that particular method. Designed to offer statistical knowledge to the non-specialist, this volume can be used in courses on research methods, or for courses on statistical applications to biological, medical, life, social, or physical sciences. It will also be useful to academic and industrial researchers in engineering and in the physical sciences who will benefit from a stronger understanding of how to analyze empirical data. The book is written for those with foundational education in calculus. However, a brief review of fundamental concepts of probability and statistics, together with a primer on some concepts in elementary calculus and matrix algebra, is included. R code and sample datasets are provided.

This book promotes and describes the application of objective and effective decision making in asset management based on mathematical models and practical techniques that can be easily implemented in organizations. This comprehensive and timely publication will be an essential reference source, building on available literature in the field of asset management while laying the groundwork for further research breakthroughs in this field. The text provides the resources necessary for managers, technology developers, scientists and engineers to adopt and implement better decision making based on models and techniques that contribute to recognizing risks and uncertainties and, in general terms, to the important role of asset management to increase competitiveness in organizations.

This volume originates from the INDAM Symposium on Trends on Applications of Mathematics to Mechanics (STAMM), which was held at the INDAM headquarters in Rome on 5-9 September 2016. It brings together original contributions at the interface of Mathematics and Mechanics. The focus is on mathematical models of phenomena issued from various applications. These include thermomechanics of solids and gases, nematic shells, thin films, dry friction, delamination, damage, and phase-field dynamics. The papers in the volume present novel results and identify possible future developments. The book is addressed to researchers involved in Mathematics and its applications to Mechanics.

Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.

This book is dedicated to Prof. Peter Young on his 70th birthday. Professor Young has been a pioneer in systems and control, and over the past 45 years he has influenced many developments in this field. This volume comprises a collection of contributions by leading experts in system identification, time-series analysis, environmetric modelling and control system design - modern research in topics that reflect important areas of interest in Professor Young's research career. Recent theoretical developments in and relevant applications of these areas are explored treating the various subjects broadly and in depth. The authoritative and up-to-date research presented here will be of interest to academic researcher in control and disciplines related to environmental research, particularly those to with water systems. The tutorial style in which many of the contributions are composed also makes the book suitable as a source of study material for graduate students in those areas.

Evidence based medicine is at the core of modern medicine. It involves the integration of individual clinical expertise with the best available clinical evidence from systematic research and patient's values and expectations. Systematic reviews offer a summary of the best available evidence. They are the most reliable and comprehensive statement about what works. Written by clinical academics from Australia, UK, USA, and Switzerland, this contributed volume introduces the readers to the principles and practice of systematic reviews and meta-analysis. It covers the various steps involved in systematic reviews including development of a focused question and the strategy for conducting a comprehensive literature search, identifying studies addressing the underlying question, assessment of heterogeneity and the risk of bias in the included studies, data extraction, and the approach to meta-analysis. Crucial issues such as selecting the model for meta-analysis, generating and interpreting forest plots, assessing the risk of publication bias, cautions in the interpretation of subgroup and sensitivity analyses, rating certainty of the evidence using GRADE guideline, and standardized reporting of meta-analysis (PRISMA) are covered in detail. Every attempt is made to keep the narrative simple and clear. Mathematical formulae are avoided as much as possible. While the focus of this book is on systematic reviews and meta-analyses of randomised controlled trials (RCTs), the gold standard of clinical research, the essentials of systematic reviews of non-RCTs, diagnostic test accuracy studies, animal studies, individual participant data meta-analysis, and network meta-analysis are also covered. Readers from all faculties of medicine will enjoy this comprehensive and reader friendly book to understand the principles and practice of systematic reviews and meta-analysis for guiding their clinical practice and research.

This book assesses various intelligent-city evaluation systems around the globe, and subsequently combines that assessment with local-government and enterprise practices to create an evaluation index system for quantifying the Intelligent City concept. In addition, the book provides the results of the CityIQ indicator ranking of intelligent cities in China and worldwide, a system that focuses on three of the most crucial aspects of urban development: the development environment, future trends, and construction and operation. After data sorting, calculation and dimensionless treatment, a score system ranging from 0 to 100 is created for ranking and analyzing cities. Providing unique strategies for promoting an intelligent city evaluation system, the book offers a valuable reference guide for intelligent-city decision-makers, as well as leaders in public urban economy, social welfare and environmental authorities.

Features Accessible to readers with a basic background in probability and statistics Covers fundamental concepts of experimental design and cause-effect relationships Introduces classical ANOVA models, including contrasts and multiple testing Provides an example-based introduction to mixed models Features basic concepts of split-plot and incomplete block designs R code available for all steps Supplementary website with additional resources and updates

This book focuses on a development for assessing mental changes using eye pupil reactions, namely extracting emotional change from the response to evaluate the viewer's interest in visual information. The pupil of the eye reacts to both brightness and emotional state, including interest, enjoyment, and mental workload. Because pupillary change is a biological signal, various artifacts influence measurements of eye images. Technical procedures are required to extract mental activities from pupillary changes, and they are summarized here step by step, although some procedures contain earlier techniques such as analog video processing. This study examines the possibility of estimating the viewer's interest and enjoyment of viewing movies by measuring the dynamic pupillary changes, blinking, and subjective interest responses. In evaluation of pupil size, there was a significant difference in pupil size between the higher and the lower shot for the degree of subject interest response in each kind of movies. The first part of the book shows a pupil reaction model for brightness changes to extract mental activities. Pupil reactions were observed for various visual stimuli in brightness changes. With regard to the characteristics of pupillary changes, a model with a three-layer neural network was developed and the performance was evaluated. Characteristics of pupil reactions during model development are summarized here. The second part examines the possibility of estimating the viewer's interest and enjoyment of television programs by measuring dynamic pupillary changes, blinking, and subjective interest responses. The final part describes a development of estimation model of pupil size for blink artifact. The model development was able to estimate pupillary changes and pupil size while the viewer was blinking and was applied to pupillary changes in viewing television programs.

One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors' research work and approach - first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory.

This monograph focuses on the construction of regression models with linear and non-linear constrain inequalities from the theoretical point of view. Unlike previous publications, this volume analyses the properties of regression with inequality constrains, investigating the flexibility of inequality constrains and their ability to adapt in the presence of additional a priori information The implementation of inequality constrains improves the accuracy of models, and decreases the likelihood of errors. Based on the obtained theoretical results, a computational technique for estimation and prognostication problems is suggested. This approach lends itself to numerous applications in various practical problems, several of which are discussed in detail The book is useful resource for graduate students, PhD students, as well as for researchers who specialize in applied statistics and optimization. This book may also be useful to specialists in other branches of applied mathematics, technology, econometrics and finance

This book presents some recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to handle a broader range of data types than those analyzed by traditional generalized linear models. One example is correlated angular data. This book provides a systematic treatment for the topic of estimating functions. Under this framework, both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to marginal models and mixed-effects models, this book covers topics on joint regression analysis based on Gaussian copulas and generalized state space models for longitudinal data from long time series. Various real-world data examples, numerical illustrations and software usage tips are presented throughout the book. This book has evolved from lecture notes on longitudinal data analysis, and may be considered suitable as a textbook for a graduate course on correlated data analysis. This book is inclined more towards technical details regarding the underlying theory and methodology used in software-based applications. Therefore, the book will serve as a useful reference for those who want theoretical explanations to puzzles arising from data analyses or deeper understanding of underlying theory related to analyses.

The fourth edition of this successful textbook presents a comprehensive introduction to statistical and numerical methods for the evaluation of empirical and experimental data. Equal weight is given to statistical theory and practical problems. The concise mathematical treatment of the subject matter is illustrated by many examples and for the present edition a library of Java programs has been developed. It comprises methods of numerical data analysis and graphical representation as well as many example programs and solutions to programming problems. The programs (source code, Java classes and documentation) and extensive appendices to the main text are available for free download from the book's page at www.springer.com.

ContentsProbabilities. Random variables.Random numbers and the Monte Carlo Method.Statistical distributions (binomial, Gauss, Poisson). Samples. Statistical tests.Maximum Likelihood. Least Squares. Regression. Minimization.Analysis of Variance. Time series analysis.

Audience

The book is conceived both as an introduction and as a work of reference. In particular it addresses itself to students, scientists and practitioners in science and engineering as a help in the analysis of their datain laboratory courses, in working for bachelor or master degrees, in thesis work, in research and professional work.

""The book is concise, but gives a sufficiently rigorous mathematical treatment of practical statistical methods for data analysis; it can be of great use to all who are involved with data analysis." "Physicalia""

.".".Serves as a nice reference guide for any scientist interested in the fundamentals of data analysis on the computer." "The American Statistician

""This lively and erudite treatise covers the theory of the main statistical tools and their practical applications...a first rate university textbook, and good background material for the practicing physicist." "Physics Bulletin

The Author

Siegmund Brandt is Emeritus Professor of Physics at the University of Siegen. With his group he worked on experiments in elementary-particle physics at the research centers DESY in Hamburg and CERN in Geneva in which the analysis of the experimental data plays an important role. He is author or coauthor of textbooks which have appeared in ten languages.