Statistical Inference for Ergodic Diffusion Processes encompasses a wealth of results from over ten years of mathematical literature. It provides a comprehensive overview of existing techniques, and presents - for the first time in book form - many new techniques and approaches. An elementary introduction to the field at the start of the book introduces a class of examples - both non-standard and classical - that reappear as the investigation progresses to illustrate the merits and demerits of the procedures. The statements of the problems are in the spirit of classical mathematical statistics, and special attention is paid to asymptotically efficient procedures. Today, diffusion processes are widely used in applied problems in fields such as physics, mechanics and, in particular, financial mathematics. This book provides a state-of-the-art reference that will prove invaluable to researchers, and graduate and postgraduate students, in areas such as financial mathematics, economics, physics, mechanics and the biomedical sciences.

Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

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.

This text is concerned primarily with the theory of linear and nonlinear programming, and a number of closely-related problems, and with algorithms appropriate to those problems. In the first part of the book, the authors introduce the concept of duality which serves as a unifying concept throughout the book. The simplex algorithm is presented along with modifications and adaptations to problems with special structures. Two alternative algorithms, the ellipsoidal algorithm and Karmarker's algorithm, are also discussed, along with numerical considerations. the second part of the book looks at specific types of problems and methods for their solution. This book is designed as a textbook for mathematical programming courses, and each chapter contains numerous exercises and examples.

How do preprocessing steps such as tokenization, stemming, and removing stop words affect predictive models? Build beginning-to-end workflows for predictive modeling using text as features Compare traditional machine learning methods and deep learning methods for text data

This book provides a thorough development of the powerful methods of heavy traffic analysis and approximations with applications to a wide variety of stochastic (e.g. queueing and communication) networks, for both controlled and uncontrolled systems. The approximating models are reflected stochastic differential equations. The analytical and numerical methods yield considerable simplifications and insights and good approximations to both path properties and optimal controls under broad conditions on the data and structure. The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest. Control problems in telecommunications and applications to scheduling, admissions control, polling, and elsewhere are treated. The necessary probability background is reviewed, including a detailed survey of reflected stochastic differential equations, weak convergence theory, methods for characterizing limit processes, and ergodic problems.

Bayesian Reliability presents modern methods and techniques for analyzing reliability data from a Bayesian perspective. The adoption and application of Bayesian methods in virtually all branches of science and engineering have significantly increased over the past few decades. This increase is largely due to advances in simulation-based computational tools for implementing Bayesian methods.

The authors extensively use such tools throughout this book, focusing on assessing the reliability of components and systems with particular attention to hierarchical models and models incorporating explanatory variables. Such models include failure time regression models, accelerated testing models, and degradation models. The authors pay special attention to Bayesian goodness-of-fit testing, model validation, reliability test design, and assurance test planning. Throughout the book, the authors use Markov chain Monte Carlo (MCMC) algorithms for implementing Bayesian analyses -- algorithms that make the Bayesian approach to reliability computationally feasible and conceptually straightforward.

This book is primarily a reference collection of modern Bayesian methods in reliability for use by reliability practitioners. There are more than 70 illustrative examples, most of which utilize real-world data. This book can also be used as a textbook for a course in reliability and contains more than 160 exercises.

Noteworthy highlights of the book include Bayesian approaches for the following:

• Goodness-of-fit and model selection methods
• Hierarchical models for reliability estimation
• Fault tree analysis methodology that supports data acquisition at all levels in the tree
• Bayesian networks in reliability analysis
• Analysis of failure count and failure time data collected from repairable systems, and the assessment of various related performance criteria
• Analysis of nondestructive and destructive degradation data
• Optimal design of reliability experiments
• Hierarchical reliability assurance testing

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

Classic biostatistics, a branch of statistical science, has as its main focus the applications of statistics in public health, the life sciences, and the pharmaceutical industry. Modern biostatistics, beyond just a simple application of statistics, is a confluence of statistics and knowledge of multiple intertwined fields. The application demands, the advancements in computer technology, and the rapid growth of life science data (e.g., genomics data) have promoted the formation of modern biostatistics. There are at least three characteristics of modern biostatistics: (1) in-depth engagement in the application fields that require penetration of knowledge across several fields, (2) high-level complexity of data because they are longitudinal, incomplete, or latent because they are heterogeneous due to a mixture of data or experiment types, because of high-dimensionality, which may make meaningful reduction impossible, or because of extremely small or large size; and (3) dynamics, the speed of development in methodology and analyses, has to match the fast growth of data with a constantly changing face. This book is written for researchers, biostatisticians/statisticians, and scientists who are interested in quantitative analyses. The goal is to introduce modern methods in biostatistics and help researchers and students quickly grasp key concepts and methods. Many methods can solve the same problem and many problems can be solved by the same method, which becomes apparent when those topics are discussed in this single volume.

As information technologies become increasingly distributed and accessible to larger number of people and as commercial and government organizations are challenged to scale their applications and services to larger market shares, while reducing costs, there is demand for software methodologies and appli- tions to provide the following features: Richer application end-to-end functionality; Reduction of human involvement in the design and deployment of the software; Flexibility of software behaviour; and Reuse and composition of existing software applications and systems in novel or adaptive ways. When designing new distributed software systems, the above broad requi- ments and their translation into implementations are typically addressed by partial complementarities and overlapping technologies and this situation gives rise to significant software engineering challenges. Some of the challenges that may arise are: determining the components that the distributed applications should contain, organizing the application components, and determining the assumptions that one needs to make in order to implement distributed scalable and flexible applications, etc.

Intended for advanced undergraduates and graduate students, this book is a practical guide to the use of probability and statistics in experimental physics. The emphasis is on applications and understanding, on theorems and techniques actually used in research. The text is not a comprehensive text in probability and statistics; proofs are sometimes omitted if they do not contribute to intuition in understanding the theorem. The problems, some with worked solutions, introduce the student to the use of computers; occasional reference is made to routines available in the CERN library, but other systems, such as Maple, can also be used. Topics covered include: basic concepts; definitions; some simple results independent of specific distributions; discrete distributions; the normal and other continuous distributions; generating and characteristic functions; the Monte Carlo method and computer simulations; multi-dimensional distributions; the central limit theorem; inverse probability and confidence belts; estimation methods; curve fitting and likelihood ratios; interpolating functions; fitting data with constraints; robust estimation methods. This second edition introduces a new method for dealing with small samples, such as may arise in search experiments, when the data are of low probability. It also includes a new chapter on queuing problems (including a simple, but useful buffer length example). In addition new sections discuss over- and under-coverage using confidence belts, the extended maximum-likelihood method, the use of confidence belts for discrete distributions, estimation of correlation coefficients, and the effective variance method for fitting y = f(x) when both x and y have measurement errors. A complete Solutions Manual is available.

This unique textbook presents a course on computational linear algebra. Offers many unique applications. MATLAB is used throughout.

Easy-to-Use Reference and Software for Statistical Modeling and Testing Handbook of Statistical Distributions with Applications, Second Edition provides quick access to common and specialized probability distributions for modeling practical problems and performing statistical calculations. Along with many new examples and results, this edition includes both the author's StatCalc software and R codes to accurately and easily carry out computations. New to the Second Edition Major changes in binomial, Poisson, normal, gamma, Weibull, exponential, logistic, Laplace, and Pareto distributions Updated statistical tests and intervals based on recent publications in statistical journals Enhanced PC calculator StatCalc with electronic help manuals R functions for cases where StatCalc is not applicable, with the codes available online This highly praised handbook integrates popular probability distribution models, formulas, applications, and software to help you compute a variety of statistical intervals. It covers probability and percentiles, algorithms for random number generation, hypothesis tests, confidence intervals, tolerance intervals, prediction intervals, sample size determination, and much more.

This book covers a range of statistical methods useful in the analysis of medical data, from the simple to the sophisticated, and shows how they may be applied using the latest versions of S-PLUS and S-PLUS 6. In each chapter several sets of medical data are explored and analysed using a mixture of graphical and model fitting approaches. At the end of each chapter the S-PLUS script files are listed, enabling readers to reproduce all the analyses and graphics in the chapter. These script files can be downloaded from a web site. The aim of the book is to show how to use S-PLUS as a powerful environment for undertaking a variety of statistical analyses from simple inference to complex model fitting, and for providing informative graphics. All such methods are of increasing importance in handling data from a variety of medical investigations including epidemiological studies and clinical trials. The mix of real data examples and background theory make this book useful for students and researchers alike. For the former, exercises are provided at the end of each chapter to increase their fluency in using the command line language of the S-PLUS software. Professor Brian Everitt is Head of the Department of Biostatistics and Computing at the Institute of Psychiatry in London and Sophia Rabe-Hesketh is a senior lecturer in the same department. Professor Everitt is the author of over 30 books on statistics including two previously co-authored with Dr. Rabe-Hesketh.

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

After Karl JAreskog's first presentation in 1970, Structural Equation Modelling or SEM has become a main statistical tool in many fields of science. It is the standard approach of factor analytic and causal modelling in such diverse fields as sociology, education, psychology, economics, management and medical sciences. In addition to an extension of its application area, Structural Equation Modelling also features a continual renewal and extension of its theoretical background. The sixteen contributions to this book, written by experts from many countries, present important new developments and interesting applications in Structural Equation Modelling. The book addresses methodologists and statisticians professionally dealing with Structural Equation Modelling to enhance their knowledge of the type of models covered and the technical problems involved in their formulation. In addition, the book offers applied researchers new ideas about the use of Structural Equation Modeling in solving their problems. Finally, methodologists, mathematicians and applied researchers alike are addressed, who simply want to update their knowledge of recent approaches in data analysis and mathematical modelling.

This book is devoted to Corrado Gini, father of the Italian statistical school. It celebrates the 50th anniversary of his death by bearing witness to the continuing extraordinary scientific relevance of his interdisciplinary interests. The book comprises a selection of the papers presented at the conference of the Italian Statistical Society, Statistics and Demography - the Legacy of Corrado Gini, held in Treviso in September 2015. The work covers many topics linked to Gini's scientific legacy, ranging from the theory of statistical inference to multivariate statistical analysis, demography and sociology. In this volume, readers will find many interesting contributions on entropy measures, permutation procedures for the heterogeneity test, robust estimation of skew-normal parameters, S-weighted estimator, measures of multidimensional performance using Gini's delta, small-sample confidence intervals for Gini's gamma index, Bayesian estimation of the Gini-Simpson index, spatial residential patterns of selected foreign groups, minority segregation processes, dynamic time warping to study cruise tourism, and financial stress spill over. This book will appeal to all statisticians, demographers, economists, and sociologists interested in the field.

The book deals with some of the fundamental issues of risk assessment in grid computing environments. The book describes the development of a hybrid probabilistic and possibilistic model for assessing the success of a computing task in a grid environment

Modelling Survival Data in Medical Research, Fourth Edition describes the analysis of survival data, illustrated using a wide range of examples from biomedical research. Written in a non-technical style, it concentrates on how the techniques are used in practice. Starting with standard methods for summarising survival data, Cox regression and parametric modelling, the book covers many more advanced techniques, including interval-censoring, frailty modelling, competing risks, analysis of multiple events, and dependent censoring. This new edition contains chapters on Bayesian survival analysis and use of the R software. Earlier chapters have been extensively revised and expanded to add new material on several topics. These include methods for assessing the predictive ability of a model, joint models for longitudinal and survival data, and modern methods for the analysis of interval-censored survival data. Features: Presents an accessible account of a wide range of statistical methods for analysing survival data Contains practical guidance on modelling survival data from the author's many years of experience in teaching and consultancy Shows how Bayesian methods can be used to analyse survival data Includes details on how R can be used to carry out all the methods described, with guidance on the interpretation of the resulting output Contains many real data examples and additional data sets that can be used for coursework All data sets used are available in electronic format from the publisher's website Modelling Survival Data in Medical Research, Fourth Edition is an invaluable resource for statisticians in the pharmaceutical industry and biomedical research centres, research scientists and clinicians who are analysing their own data, and students following undergraduate or postgraduate courses in survival analysis.

Provides a comprehensive and accessible introduction to general insurance pricing, based on the author’s many years of experience as both a teacher and practitioner. Suitable for students taking a course in general insurance pricing, notably if they are studying to become an actuary through the UK Institute of Actuaries exams. No other title quite like this on the market that is perfect for teaching/study, and is also an excellent guide for practitioners.

Linear regression is an important area of statistics, theoretical or applied. There have been a large number of estimation methods proposed and developed for linear regression. Each has its own competitive edge but none is good for all purposes. This manuscript focuses on construction of an adaptive combination of two estimation methods. The purpose of such adaptive methods is to help users make an objective choice and to combine desirable properties of two estimators.

INSTANT NEW YORK TIMES BESTSELLER "A new masterpiece from one of my favorite authors... [How The World Really Works] is a compelling and highly readable book that leaves readers with the fundamental grounding needed to help solve the world's toughest challenges."-Bill Gates "Provocative but perceptive . . . You can agree or disagree with Smil-accept or doubt his 'just the facts' posture-but you probably shouldn't ignore him."-The Washington Post An essential analysis of the modern science and technology that makes our twenty-first century lives possible-a scientist's investigation into what science really does, and does not, accomplish. We have never had so much information at our fingertips and yet most of us don't know how the world really works. This book explains seven of the most fundamental realities governing our survival and prosperity. From energy and food production, through our material world and its globalization, to risks, our environment and its future, How the World Really Works offers a much-needed reality check-because before we can tackle problems effectively, we must understand the facts. In this ambitious and thought-provoking book we see, for example, that globalization isn't inevitable-the foolishness of allowing 70 per cent of the world's rubber gloves to be made in just one factory became glaringly obvious in 2020-and that our societies have been steadily increasing their dependence on fossil fuels, such that any promises of decarbonization by 2050 are a fairy tale. For example, each greenhouse-grown supermarket-bought tomato has the equivalent of five tablespoons of diesel embedded in its production, and we have no way of producing steel, cement or plastics at required scales without huge carbon emissions. Ultimately, Smil answers the most profound question of our age: are we irrevocably doomed or is a brighter utopia ahead? Compelling, data-rich and revisionist, this wonderfully broad, interdisciplinary guide finds faults with both extremes. Looking at the world through this quantitative lens reveals hidden truths that change the way we see our past, present and uncertain future.

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. Limit theorems for semimartingales form the basis of the martingale approximation approach. The methods of martingale approximation addressed in this book pertain to estimates of the rate of convergence in the central limit theorem and in the invariance principle. Some applications of martingale approximation are illustrated by the analysis of U-statistics, rank statistics, statistics of exchangeable variables and stochastic exponential statistics. Simplified results of stochastic analysis are given for use in investigations of many applied problems, including mathematical statistics, financial mathematics, mathematical biology, industrial mathematics and engineering.

In 1978 Edwin T. Jaynes and Myron Tribus initiated a series of workshops to exchange ideas and recent developments in technical aspects and applications of Bayesian probability theory. The first workshop was held at the University of Wyoming in 1981 organized by C.R. Smith and W.T. Grandy. Due to its success, the workshop was held annually during the last 18 years. Over the years, the emphasis of the workshop shifted gradually from fundamental concepts of Bayesian probability theory to increasingly realistic and challenging applications. The 18th international workshop on Maximum Entropy and Bayesian Methods was held in Garching / Munich (Germany) (27-31. July 1998). Opening lectures by G. Larry Bretthorst and by Myron Tribus were dedicated to one of th the pioneers of Bayesian probability theory who died on the 30 of April 1998: Edwin Thompson Jaynes. Jaynes revealed and advocated the correct meaning of 'probability' as the state of knowledge rather than a physical property. This inter pretation allowed him to unravel longstanding mysteries and paradoxes. Bayesian probability theory, "the logic of science" - as E.T. Jaynes called it - provides the framework to make the best possible scientific inference given all available exper imental and theoretical information. We gratefully acknowledge the efforts of Tribus and Bretthorst in commemorating the outstanding contributions of E.T. Jaynes to the development of probability theory."