Covers the key issues required for students wishing to understand and analyse the core empirical issues in economics. It focuses on descriptive statistics, probability concepts and basic econometric techniques and has an accompanying website that contains all the data used in the examples and provides exercises for undertaking original research.

This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.

This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

Between Certainty & Uncertainty is a one-of a-kind short course on statistics for students, engineers and researchers. It is a fascinating introduction to statistics and probability with notes on historical origins and 80 illustrative numerical examples organized in the five units:

. Chapter 1 "Descriptive Statistics" Compressing small samples, basic averages - mean and variance, their main properties including God s proof; linear transformations and "z-scored" statistics .

. Chapter 2 "Grouped data" Udny Yule s concept of qualitative and quantitative variables. Grouping these two kinds of data. Graphical tools. Combinatorial rules and qualitative variables. Designing frequency histogram. Direct and coded evaluation of quantitative data. Significance of percentiles.

. Chapter 3 "Regression and correlation" Geometrical distance and equivalent distances in two orthogonal directions as a prerequisite to the concept of two regression lines. Misleading in interpreting two regression lines. Derivation of the two regression lines. Was Hubble right? Houbolt s cloud. What in fact measures the correlation coefficient?

. Chapter 4 "Binomial distribution" Middle ages origins of the binomials; figurate numbers and combinatorial rules. Pascal s Arithmetical Triangle. Bernoulli s or Poisson Trials? John Arbuthnot curing binomials. How Newton taught S. Pepys probability. Jacob Bernoulli s Weak Law of Large Numbers and others.

. Chapter 5 "Normal distribution and binomial heritage" Tables of the normal distribution. Abraham de Moivre and the second theorem of de Moivre-Laplace.

. Chapter 1 "Descriptive Statistics" Compressing small samples, basic averages - mean and variance, their main properties including God s proof; linear transformations and "z-scored" statistics .

. Chapter 2 "Grouped data" Udny Yule s concept of qualitative and quantitative variables. Grouping these two kinds of data. Graphical tools. Combinatorial rules and qualitative variables. Designing frequency histogram. Direct and coded evaluation of quantitative data. Significance of percentiles.

. Chapter 3 "Regression and correlation" Geometrical distance and equivalent distances in two orthogonal directions as a prerequisite to the concept of two regression lines. Misleading in interpreting two regression lines. Derivation of the two regression lines. Was Hubble right? Houbolt s cloud. What in fact measures the correlation coefficient?

. Chapter 4 "Binomial distribution" Middle ages origins of the binomials; figurate numbers and combinatorial rules. Pascal s Arithmetical Triangle. Bernoulli s or Poisson Trials? John Arbuthnot curing binomials. How Newton taught S. Pepys probability. Jacob Bernoulli s Weak Law of Large Numbers and others.

. Chapter 5 "Normal distribution and binomial heritage" Tables of the normal distribution. Abraham de Moivre and the second theorem of de Moivre-Laplace.

. Chapter 5 "Normal distribution and binomial heritage" Tables of the normal distribution. Abraham de Moivre and the second theorem of de Moivre-Laplace.

"

This volume, which highlights recent advances in statistical methodology and applications, is divided into two main parts. The first part presents theoretical results on estimation techniques in functional statistics, while the second examines three key areas of application: estimation problems in queuing theory, an application in signal processing, and the copula approach to epidemiologic modelling. The book's peer-reviewed contributions are based on papers originally presented at the Marrakesh International Conference on Probability and Statistics held in December 2013.

Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications. These review/exploratory chapters present recent and current research on stochastic orders reported at the International Workshop on Stochastic Orders in Reliability and Risk Management, or SORR2011, which took place in the City Hotel, Xiamen, China, from June 27 to June 29, 2011. The conference's talks and invited contributions also represent the celebration of Professor Moshe Shaked, who has made comprehensive, fundamental contributions to the theory of stochastic orders and its applications in reliability, queueing modeling, operations research, economics and risk analysis. This volume is in honor of Professor Moshe Shaked. The work presented in this volume represents active research on stochastic orders and multivariate dependence, and exemplifies close collaborations between scholars working in different fields. The Xiamen Workshop and this volume seek to revive the community workshop tradition on stochastic orders and dependence and strengthen research collaboration, while honoring the work of a distinguished scholar.

This is the first statistics text to address the unique issues the Marine Affairs professional and student must confront. Marine and coastal resource management is unique in that problem solutions increasingly demand an interdisciplinary approach using data from both the social and natural sciences. This is the first statistics text that addresses marine resource problems using both non-parametric and parametric techniques in a non-intimidating fashion. This is the first statistics text that addresses the unique issues the Marine Affairs professional and student must confront. Since so many of the problems faced by environmental managers are interdisciplinary, involving data and information from a host of disciplines including both natural and social sciences, this volume includes a selected number of both parametric and non-parametric statistical models. The selection of methods has been guided by the type of problems Marine Affairs professionals deal with on a day-to-day basis. The text is written for the non-mathematical reader who may have little or no prior experience in statistics or advanced mathematics. Each chapter is divided into two sections, one which describes the method, followed by one or two fully worked out examples, and concludes with a lab for student use. This volume will be of value to students and professionals involved with the description, analysis, and evaluation of coastal and marine resource issues.

This book explores different approaches to defining the concept of region depending on the specific question that needs to be answered. While the typical administrative spatial data division fits certain research questions well, in many cases, defining regions in a different way is fundamental in order to obtain significant empirical evidence. The book is divided into three parts: The first part is dedicated to a methodological discussion of the concept of region and the different potential approaches from different perspectives. The problem of having sufficient information to define different regional units is always present. This justifies the second part of the book, which focuses on the techniques of ecological inference applied to estimating disaggregated data from observable aggregates. Finally, the book closes by presenting several applications that are in line with the functional areas definition in regional analysis.

The main body of this book is devoted to statistical physics, whereas much less emphasis is given to thermodynamics. In particular, the idea is to present the most important outcomes of thermodynamics - most notably, the laws of thermodynamics - as conclusions from derivations in statistical physics. Special emphasis is on subjects that are vital to engineering education. These include, first of all, quantum statistics, like the Fermi-Dirac distribution, as well as diffusion processes, both of which are fundamental to a sound understanding of semiconductor devices. Another important issue for electrical engineering students is understanding of the mechanisms of noise generation and stochastic dynamics in physical systems, most notably in electric circuitry. Accordingly, the fluctuation-dissipation theorem of statistical mechanics, which is the theoretical basis for understanding thermal noise processes in systems, is presented from a signals-and-systems point of view, in a way that is readily accessible for engineering students and in relation with other courses in the electrical engineering curriculum, like courses on random processes.

Chi-Squared Goodness of Fit Tests with Applications provides a thorough and complete context for the theoretical basis and implementation of Pearson s monumental contribution and its wide applicability for chi-squared goodness of fit tests. The book is ideal for researchers and scientists conducting statistical analysis in processing of experimental data as well as to students and practitioners with a good mathematical background who use statistical methods. The historical context, especially Chapter 7, provides great insight into importance of this subject with an authoritative author team. This reference includes the most recent application developments in using these methods and models.
Systematic presentation with interesting historical context and coverage of the fundamentals of the subjectPresents modern model validity methods, graphical techniques, and computer-intensive methodsRecent research and a variety of open problemsInteresting real-life examples for practitioners"

This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

This book provides an introduction to operational research methods and their application in the agrifood and environmental sectors. It explains the need for multicriteria decision analysis and teaches users how to use recent advances in multicriteria and clustering classification techniques in practice. Further, it presents some of the most common methodologies for statistical analysis and mathematical modeling, and discusses in detail ten examples that explain and show “hands-on” how operational research can be used in key decision-making processes at enterprises in the agricultural food and environmental industries. As such, the book offers a valuable resource especially well suited as a textbook for postgraduate courses.

The papers in this volume represent a broad, applied swath of advanced contributions to the 2015 ICSA/Graybill Applied Statistics Symposium of the International Chinese Statistical Association, held at Colorado State University in Fort Collins. The contributions cover topics that range from statistical applications in business and finance to applications in clinical trials and biomarker analysis. Each papers was peer-reviewed by at least two referees and also by an editor. The conference was attended by over 400 participants from academia, industry, and government agencies around the world, including from North America, Asia, and Europe.

The only comprehensive guide to the theory and practice of one of today's most important probabilistic techniques
The past 15 years have witnessed many significant advances in sequential estimation, especially in the areas of three-stage and nonparametric methodology. Yet, until now, there were no references devoted exclusively to this rapidly growing statistical field.
Sequential Estimation is the first, single-source guide to the theory and practice of both classical and modern sequential estimation techniques--including parametric and nonparametric methods. Researchers in sequential analysis will appreciate the unified, logically integrated treatment of the subject, as well as coverage of important contemporary procedures not covered in more general sequential analysis texts, such as:
* Shrinkage estimation
* Empirical and hierarchical Bayes procedures
* Multistage sampling and accelerated sampling procedures
* Time-sequential estimation
* Sequential estimation in finite population sampling
* Reliability estimation and capture-recapture methodologies leading to sequential tagging schemes

An indispensable resource for researchers in sequential analysis, Sequential Estimation is an ideal graduate-level text as well.

Risk management for financial institutions is one of the key topics the financial industry has to deal with. The present volume is a mathematically rigorous text on solvency modeling. Currently, there are many new developments in this area in the financial and insurance industry (Basel III and Solvency II), but none of these developments provides a fully consistent and comprehensive framework for the analysis of solvency questions. Merz and Wuthrich combine ideas from financial mathematics (no-arbitrage theory, equivalent martingale measure), actuarial sciences (insurance claims modeling, cash flow valuation) and economic theory (risk aversion, probability distortion) to provide a fully consistent framework. Within this framework they then study solvency questions in incomplete markets, analyze hedging risks, and study asset-and-liability management questions, as well as issues like the limited liability options, dividend to shareholder questions, the role of re-insurance, etc. This work embeds the solvency discussion (and long-term liabilities) into a scientific framework and is intended for researchers as well as practitioners in the financial and actuarial industry, especially those in charge of internal risk management systems. Readers should have a good background in probability theory and statistics, and should be familiar with popular distributions, stochastic processes, martingales, etc.

This volume reviews and summarizes some of A. I. McLeod's significant contributions to time series analysis. It also contains original contributions to the field and to related areas by participants of the festschrift held in June 2014 and friends of Dr. McLeod. Covering a diverse range of state-of-the-art topics, this volume well balances applied and theoretical research across fourteen contributions by experts in the field. It will be of interest to researchers and practitioners in time series, econometricians, and graduate students in time series or econometrics, as well as environmental statisticians, data scientists, statisticians interested in graphical models, and researchers in quantitative risk management.

Although there are many books on mathematical finance, few deal with the statistical aspects of modern data analysis as applied to financial problems. This textbook fills this gap by addressing some of the most challenging issues facing financial engineers. It shows how sophisticated mathematics and modern statistical techniques can be used in the solutions of concrete financial problems. Concerns of risk management are addressed by the study of extreme values, the fitting of distributions with heavy tails, the computation of values at risk (VaR), and other measures of risk. Principal component analysis (PCA), smoothing, and regression techniques are applied to the construction of yield and forward curves. Time series analysis is applied to the study of temperature options and nonparametric estimation. Nonlinear filtering is applied to Monte Carlo simulations, option pricing and earnings prediction. This textbook is intended for undergraduate students majoring in financial engineering, or graduate students in a Master in finance or MBA program. It is sprinkled with practical examples using market data, and each chapter ends with exercises. Practical examples are solved in the R computing environment. They illustrate problems occurring in the commodity, energy and weather markets, as well as the fixed income, equity and credit markets.The examples, experiments and problem setsare based on the library Rsafd developed for the purpose of the text. The book should help quantitative analysts learn and implement advanced statistical concepts. Also, it will be valuable for researchers wishing to gain experience with financial data, implement and test mathematical theories, and address practical issues that are often ignored or underestimated in academic curricula.

This is the new, fully-revised edition to the book "Statistical Analysis of Financial Data in S-Plus."

Rene Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering, and Director of Graduate Studies of the Bendheim Center for Finance. His publications include over one hundred articles and eight books in probability and statistics. He was elected Fellow of the Institute of Mathematical Statistics in 1984, and of the Society for Industrial and Applied Mathematics in 2010. He is on the editorial boardof several peer-reviewed journals and book series. Professor Carmona has developed computer programs for teaching statistics and research in signal analysis and financial engineering. He has workedfor many years on energy, the commodity markets and more recently in environmental economics, and he is recognized as a leadingresearcher and expert in these areas."

This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.
A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebrasin thatalgebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.
Written in a clear, concise and direct manner, "Non-Commutative Multiple-Valued Logic Algebras" will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science."

This is a unique book addressing the integration of risk methodology from various fields. It will stimulate intellectual debate and communication across disciplines, promote better risk management practices and contribute to the development of risk management methodologies. Individual chapters explain fundamental risk models and measurement, and address risk and security issues from diverse areas such as finance and insurance, the health sciences, life sciences, engineering and information science. Integrated Risk Sciences is an emerging discipline that considers risks in different fields, aiming at a common language, and at sharing and improving methods developed in different fields. Readers should have a Bachelor degree and have taken at least one basic university course in statistics and probability. The main goal of the book is to provide basic knowledge on risk and security in a common language; the authors have taken particular care to ensure that all content can readily be understood by doctoral students and researchers across disciplines. Each chapter provides simple case studies and examples, open research questions and discussion points, and a selected bibliography inviting readers to further study.

This volume, based on the Russian edition publised in 1980, presents the fundamentals of mathematical geology. New developments which have taken place in the last ten years or so have been taken into account as far as possible, and this English edition contains two new chapters devoted, respectively, to random processes and a survey of future geological problems. The book has eight chapters. Chapter one deals with the basic question "what is mathematical geology?" Chapter two deals with the concept of probability. Chapter three relates this fundamental tool to geological problems with the help of specific examples. Chapters four through six cover the theory of random sequence and concentrates on the form which is the most useful to geologists. Chapter seven is dedicated to continuous Markov processes which occur frequently in geological phenomena. The volume concludes with an overview of ideas which have been generated by mathematical geology and which pave the way for the further development of the subject.

This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not easily found in a single text are provided, such as connections between control theory and mathematical finance, as well as differential games. The book is self-contained and prioritizes concepts rather than full rigor, targeting scientists who want to use control theory in their research in applied mathematics, engineering, economics, and management science. Examples and exercises are included throughout, which will be useful for PhD courses and graduate courses in general.Dr. Alain Bensoussan is Lars Magnus Ericsson Chair at UT Dallas and Director of the International Center for Decision and Risk Analysis which develops risk management research as it pertains to large-investment industrial projects that involve new technologies, applications and markets. He is also Chair Professor at City University Hong Kong.

This book covers some recent developments in statistical inference. The author's main aim is to develop a theory of generalized p-values and generalized confidence intervals and to show how these concepts may be used to make exact statistical inferences in a variety of practical applications. In particular, they provide methods applicable in problems involving nuisance parameters such as those encountered in comparing two exponential distributions or in ANOVA without the assumption of equal error variances. The generalized procedures are shown to be more powerful in detecting significant experimental results and in avoiding misleading conclusions.

This book contains entirely new results, not to be found elsewhere. Furthermore, additional results scattered elsewhere in the literature are clearly presented. Several well-known distributions such as Weibull distributions, exponentiated Burr type XII distributions and exponentiated exponential distributions and their properties are demonstrated. Analysis of real as well as well-simulated data are analyzed. A number of inferences based on a finite mixture of distributions are also presented.

This book presents classical Markov Decision Processes (MDP) for real-life applications and optimization. MDP allows users to develop and formally support approximate and simple decision rules, and this book showcases state-of-the-art applications in which MDP was key to the solution approach. The book is divided into six parts. Part 1 is devoted to the state-of-the-art theoretical foundation of MDP, including approximate methods such as policy improvement, successive approximation and infinite state spaces as well as an instructive chapter on Approximate Dynamic Programming. It then continues with five parts of specific and non-exhaustive application areas. Part 2 covers MDP healthcare applications, which includes different screening procedures, appointment scheduling, ambulance scheduling and blood management. Part 3 explores MDP modeling within transportation. This ranges from public to private transportation, from airports and traffic lights to car parking or charging your electric car . Part 4 contains three chapters that illustrates the structure of approximate policies for production or manufacturing structures. In Part 5, communications is highlighted as an important application area for MDP. It includes Gittins indices, down-to-earth call centers and wireless sensor networks. Finally Part 6 is dedicated to financial modeling, offering an instructive review to account for financial portfolios and derivatives under proportional transactional costs. The MDP applications in this book illustrate a variety of both standard and non-standard aspects of MDP modeling and its practical use. This book should appeal to readers for practitioning, academic research and educational purposes, with a background in, among others, operations research, mathematics, computer science, and industrial engineering.

This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. The stakes are high and the reader determines the outcome. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. This works in conjunction with the bayess package.

Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels, as exemplified by courses given at Universite Paris Dauphine (France), University of Canterbury (New Zealand), and University of British Columbia (Canada). It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics. A strength of the text is the noteworthy emphasis on the role of models in statistical analysis.

This is the new, fully-revised edition to the book Bayesian Core: A Practical Approach to Computational Bayesian Statistics.

Jean-Michel Marin is Professor of Statistics at Universite Montpellier 2, France, and Head of the Mathematics and Modelling research unit. He has written over 40 papers on Bayesian methodology and computing, as well as worked closely with population geneticists over the past ten years.

Christian Robert is Professor of Statistics at Universite Paris-Dauphine, France. He has written over 150 papers on Bayesian Statistics and computational methods and is the author or co-author of seven books on those topics, including The Bayesian Choice (Springer, 2001), winner of the ISBA DeGroot Prize in 2004. He is a Fellow of the Institute of Mathematical Statistics, the Royal Statistical Society and the American Statistical Society. He has been co-editor of the Journal of the Royal Statistical Society, Series B, and in the editorial boards of the Journal of the American Statistical Society, the Annals of Statistics, Statistical Science, and Bayesian Analysis. He is also a recipient of an Erskine Fellowship from the University of Canterbury (NZ) in 2006 and a senior member of the Institut Universitaire de France (2010-2015)."