Probability and statistics Books
Springer Bayesian Nonparametric Statistics
Book Synopsis
£49.49
Springer Nonlinear Investing A Quantamental Approach
Book SynopsisChapter 1 Introduction.- Chapter 2 Quantamental Analysis.- Chapter 3 Nonlinear Factor Effects on Returns.- Chapter 4 Nonlinear Alpha Modeling.- Chapter 5 Tail Portfolios.- Chapter 6 Nonlinear Investing: Japan Stock Selection Strategy.- Chapter 7 Nonlinear Investing: Currency.- Chapter 9 Nonlinear Investing: Commodity.- Index.
£113.99
Springer International Publishing AG A First Course in Complex Analysis
Book SynopsisThis book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level. It introduces the exponential function very early but does so rigorously. It covers the usual topics of functions, differentiation, analyticity, contour integration, the theorems of Cauchy and their many consequences, Taylor and Laurent series, residue theory, the computation of certain improper real integrals, and a brief introduction to conformal mapping. Throughout the text an emphasis is placed on geometric properties of complex numbers and visualization of complex mappings.Table of ContentsPreface.- Acknowledgments.- Basics of Complex Numbers.- Functions of a Complex Variable.- Differentiation.- Contour Integration.- Cauchy Theory.- Series.- Residues.- Conformal Mapping.- Author's Biography.- Index.
£47.49
Springer Survival Analysis
Book SynopsisChapter 1. Introduction.- Chapter 2. Current Status Censoring.- Chapter 3. Right-Censoring.- Chapter 4. References.
£33.24
Birkhäuser Locally Perturbed Random Walks
Book SynopsisChapter 1: Introduction.- Chapter 2: Levy-type processes with singularities.- Chapter 3: Functional limit theorems for locally perturbed random walks.- Chapter 4: Auxiliary results.
£44.99
Springer Advanced Portfolio Optimization
Book SynopsisChapter 1 Introduction.- Chapter 2 Why use Python?.- Part I Parameter Estimation.- Chapter 3 Sample Based Methods.- Chapter 4 Risk Factors Models.- Chapter 5 Black Litterman Models.- Chapter 7 Convex Risk Measures.- Chapter 8 Return-Risk Trade-Off Optimization.- Chapter 9 Real Features Constraints.- Chapter 10 Risk Parity Optimization.- Chapter 11 Robust Optimization.- Part III Machine Learning Portfolio Optimization.- Chapter 12 Hierarchical Clustering Portfolios.- Chapter 13 Graph Theory Based Portfolios.- Part IV Backtesting.- Chapter 14 Generation of Synthetic Data.- Chapter 15 Backtesting Process.- Part V Appendix.- Chapter A Linear Algebra.- Chapter B Convex Optimization.- Chapter C Mixed Integer Programming.
£85.49
Springer Statistical Learning in Genetics
Book Synopsis- 1. Overview.- Part I: Fitting Likelihood and Bayesian Models.- 2. Likelihood.- 3. Computing the Likelihood.- 4. Bayesian Methods.- 5. McMC in Practice.- Part II: Prediction.- 6. Fundamentals of Prediction.- 7. Shrinkage Methods.- 8. Digression on Multiple Testing: False Discovery Rates.- 9. Binary Data.- 10. Bayesian Prediction and Model Checking.- 11. Nonparametric Methods: A Selected Overview.- Part III: Exercises and Solutions.- 12. Exercises.- 13. Solution to Exercises.
£142.49
Springer Basic Principles of Applied Medical Statistics
Book Synopsis- 1. Introduction.- 2. Descriptive Statistics.- 3. Basic Principles of Explanatory Statistics.- 4. The Analysis of a Continuous Outcome Variable.- 5. The Analysis of a Dichotomous Outcome Variable.- 6. The Analysis of Survival Data.- 7. Multiple Regression Analysis – Association Models and Prediction Models.- 8. Machine Learning.- 9. Other Outcome Variables.- 10. Missing Data.- 11. Pitfalls in (Multiple) Regression Analysis.- 12. Miscellaneous.- 13. Overview.- 14. Example Datasets.
£98.99
£16.14
Springer Robust Statistics Through the Monitoring Approach
Book SynopsisPreface.- Introduction and the Grand Plan.- Introduction to M-Estimation for Univariate Samples.- Robust Estimators in Multiple Regression.- The Monitoring Approach in Multiple Regression.- Practical Comparison of the Different Estimators.- Transformations.- Non-parametric Regression.- Extensions of the Multiple Regression Model.- Model selection.- Some Robust Data Analyses.- Software and Datasets.- Solutions.- References.- Author Index.
£44.99
Springer Coupling and Ergodic Theorems for SemiMarkovType Processes I
Book SynopsisPreface.- Introduction.- Coupling for Random Variables.- Coupling and Ergodic Theorems for Finite Markov Chains.- Coupling and Ergodic Theorems for General Markov Chains.- Hitting Times and Method of Test Functions.- Approaching of Renewal Schemes.- Synchronizing of Shifted Renewal Schemes.- Coupling for Renewal Schemes.- Coupling and Ergodic Theorems for Regenerative Processes.- Uniform Ergodic Theorems for Regenerative Processes.- Generalized Ergodic Theorems for Regenerative Processes.- Coupling and the Renewal Theorem.- Appendix A. Basic Ergodic Theorems for Regenerative Processes.- Appendix B. Methodological and Bibliographical Notes.- References.- Index.
£161.99
Springer Hybrid Switching Diffusions
Book SynopsisChapter 1 Introduction and Motivation.- Chapter 2 Switching Diffusion.- Chapter 3 Recurrence.- Chapter 4 Ergodicity.- Chapter 5 Numerical Approximation.- Chapter 6 Stability.- Chapter 7 Stability of Switching ODEs.- Chapter 8 Invariance Principles.- Chapter 9 Two-Time-Scale Switching Diffusions.- Chapter 10 Switching Jump Diffusions: Time-Scale Separations.- Chapter 11 Past-Dependent Switching Diffusion.- Chapter 12 Population Dynamics Modeled by Switching Diffusion.- Appendix.- References.- Index.
£116.99
Birkhäuser XIV Symposium on Probability and Stochastic Processes
Book SynopsisThe geometry of the deep linear network.- An introduction to the stochastic heat equation: global existence and blowup.- On the number of crossings in a random labelled tree.- Crossing bridges between percolation models and Bienaymé-Galton-Watson trees.- Asymptotic equivalence of CP Toeplitz maps.- On the analytical approach to infinite-mode Boson-Gaussian states.- Limit theorems for Randic index for Erdös-Rényi graphs.- On stationary Nash equilibria in ARAT games with unbounded payoff functions.- Anti-concentration inequalities for log-concave variables on the real line.- Time-varying discrete-time mean-field games under a discounted criterion.- The frequency process in a non-neutral two-type continuous-state branching process with competition and its genealogy.
£161.99
Springer An Introduction to Web Mining
Book Synopsis- Part I: Context, Relevance, and the Basics.- 1. Introduction.- 2. The Internet as a Data Source.- Part II: Web Technologies and Automated Data Extraction.- 3. Web 1.0 Technologies: The Static Web.- 4. Web Scraping: Data Extraction from Websites.- 5. Web 2.0 Technologies: The Programmable/Dynamic Web.- 6. Extracting Data From The Programmable Web.- 7. Data Extraction from Dynamic Websites.- Part III: Advanced Topics in Web Mining.- 8. Web Mining Programs.- 9. Crawler Implementation.- 10. Appearance and Authentication.- 11. Scaling Web Mining in the Cloud.- 12. AI Tools for Web Mining: Overview and Outlook.- Part IV: Ethical, Legal, and Scientific Rigor.- 13. Ethics and Legal Considerations.- 14. Web Mining and Scientific Rigor.
£85.49
Springer Bayesian CostEffectiveness Analysis with the R package BCEA
Book Synopsis- 1. Bayesian Analysis in Health Economics.- 2. Case Studies.- 3. BCEA — A R Package for Bayesian Cost-Effectiveness Analysis.- 4. Probabilistic Sensitivity Analysis using BCEA.- 5. BCEAweb: A User-Friendly Web-App to use BCEA.
£67.49
De Gruyter Stochastic Calculus of Variations: For Jump
Book SynopsisThis book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.
£147.72
De Gruyter Loss Data Analysis: The Maximum Entropy Approach
Book Synopsis This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences. On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems. The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable. ContentsIntroductionFrequency modelsIndividual severity modelsSome detailed examplesSome traditional approaches to the aggregation problemLaplace transforms and fractional moment problemsThe standard maximum entropy methodExtensions of the method of maximum entropySuperresolution in maxentropic Laplace transform inversionSample data dependenceDisentangling frequencies and decompounding lossesComputations using the maxentropic densityReview of statistical procedures
£56.70
de Gruyter NonStationary Stochastic Processes Estimation
Book Synopsis
£76.00
De Gruyter Modelling Stochastic Uncertainties
Book Synopsis
£74.58
de Gruyter Lehrbuch Der Wahrscheinlichkeitsrechnung
Book Synopsis
£126.64
de Gruyter Lineare Statistische Methoden Und Ihre
Book Synopsis
£126.64
de Gruyter Handbuch Zur Theorie
Book Synopsis
£126.64
de Gruyter Handbuch Zur Anwendung
Book Synopsis
£126.64
de Gruyter Statistische Inferenz Für Lineare Parameter
Book Synopsis
£126.64
Birkhauser Verlag AG Introduction to Probability with Statistical
Book SynopsisNow in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics.Key features in new edition:* 35 new exercises* Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples* New section on regression* Online instructors' manual containing solutions to all exercises<Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications.Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. … the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ … Each new concept is clearly explained and is followed by many detailed examples. … numerous examples of calculations are given and proofs are well-detailed." (Sophie Lemaire, Mathematical Reviews, Issue 2008 m)Trade Review“Schay (emer., Univ. of Massachusetts) has created a text for a two semester, calculus-based course in mathematical statistics. … The prose reads well. Physical production is good. … Summing Up: Recommended. Upper-division undergraduates and graduate students.” (W. R. Lee, Choice, Vol. 54 (6), February, 2017)“I believe that students concentrating in mathematics and related subjects will find this book readable and interesting. … I think that students learning the probability for the first time will get real value out of working through the examples and exercises of the text. … Introduction to Probability with Statistical Applications is very clearly written and reading the book is enjoyable. I would certainly recommend Schay’s book as a primary textbook for an undergraduate course in calculus-based probability.” (Jason M. Graham, MAA Reviews, September, 2016)Table of ContentsIntroduction.- The Algebra of Events.- Combinatorial Problems.- Probabilities.- Random Variables.- Expectation, Variance, Moments.- Some Special Distributions.- The Elements of Mathematical Statistics.
£61.74
Springer International Publishing AG Œuvres Complètes—Collected Works
Book SynopsisThis book contains all of Wolfgang Doeblin's publications. In addition, it includes a reproduction of the pli cacheté on l'équation de Kolmogoroff and previously unpublished material that Doeblin wrote in 1940. The articles are accompanied by commentaries written by specialists in Doeblin's various areas of interest. The modern theory of probability developed between the two World Wars thanks to the very remarkable work of Kolmogorov, Khinchin, S.N. Bernstein, Romanovsky, von Mises, Hostinsky, Onicescu, Fréchet, Lévy and others, among whom one name shines particularly brightly, that of Wolfgang Doeblin (1915–1940). The work of this young mathematician, whose life was tragically cut short by the war, remains even now, and indeed will remain into the future, an exemplar of originality and of mathematical power. This book was conceived and in essence brought to fruition by Marc Yor before his death in 2014. It is dedicated to him.Trade Review“It attracted interest not only by mathematicians or some probability theory specialists, but also by the public, which normally would not be that interested in mathematics. … the editors gathered not only all published articles of W. Doeblin, but also some more papers, especially the ‘cahier jaune’ (yellow notebook). In comments and annotations the contents of the papers are put into today’s context by probability theory specialists. The book is excellent, a large and substantial work.” (Silke Göbel, zbMATH 1460.01019, 2021)Table of ContentsJ.-M. Bismut, Avant-propos.- H. Föllmer, Geleitwort.- B. Bru, Preface.- Part I The Life of Wolfgang Doeblin March 17, 1915 – June 21, 1940: B. Bru, Biographical Summary.- W. Doeblin, Autobiographical Note.- W. Doeblin (with remarks by B. Bru and E. Seneta), Notice sur les travaux.- List of Works of Wolfgang Doeblin.- Conversion Table.- T. Lindvall, W. Doeblin 1915–1940.- B. Bru and M. Yor, La vie de Doeblin et le pli cacheté 11.668.- B. Bru and M. Yor, Comments on the Life and Mathematical Legacy of Wolfgang Doeblin.-B. Bru and E. Seneta, Two Letters of W. Doeblin to A. N. Kolmogorov.- Part II Markov Chains: E. Seneta, Doeblin on Discrete Markov Chains.- M. Iosifescu, On Doeblin and Fortet’s paper “Sur des chaînes à liaisons complètes”.- M. Iosifescu, On Doeblin’s paper “Remarques sur la théorie métrique des fractions continues”.- E. Nummelin, Doeblin’s Theory of Markov Chains on a General Measurable State Space.- W. Doeblin, Sur les chaînes discrètes de Markoff [1936b].- W. Doeblin, Errata 1: Sur les chaînes discrètes de Markoff [1936c].- W. Doeblin, Errata 2: Sur les chaînes discrètes de Markoff [1936d].- W. Doeblin, Sur les chaînes de Markoff [1936e].- W. Doeblin and R. Fortet, Sur deux notes de MM. Kryloff et Bogoliouboff [1937e].- W. Doeblin, Éléments d’une théorie générale des chaînes constantes simples de Markoff [1937f].- W. Doeblin, Le cas discontinu des probabilités en chaîne [1937a].- W. Doeblin, Sur le cas continu des probabilités en chaîne [1937b].- W. Doeblin, and Robert Fortet Sur des chaînes à liaisons complètes [1937c].- W. Doeblin, Sur l’équation de Smoluchowsky [1937d].- W. Doeblin, Sur les propriétés asymptotiques de mouvements régis par certains types de chaînes simples [1938g] (reprint of [1937g] and [1937h]).- W. Doeblin, Sur l’équation matricielle A(t+s) = [A(t)A(s)] et ses applications aux probabilités en chaîne [1938a].-W. Doeblin, Sur l’équation matricielle A(t+s) = [A(t)A(s)] et ses applications au calcul des probabilités [1940a].- W. Doeblin, Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables [1938f].- W. Doeblin, Exposé de la théorie des chaînes simples constantes de Markoff à un nombre fini d’états [1938e].- W. Doeblin, Remarques sur la théorie métrique des fractions continues [1940d.- W. Doeblin, Éléments d’une théorie générale des chaînes simples constantes de Markoff [1940e].- Part III Sums of Independent Random Variables: D. M. Mason, Notes on Wolfgang Doeblin’s 1940 paper: L’ensemble de puissances d’une loi de probabilité.- W. Doeblin and P. Lévy, Sur les sommes de variables aléatoires indépendantes à dispersions bornées inférieurement [1936a].- W. Doeblin, Premiers éléments d’une étude systématique de l’ensemble de puissances d’une loi de probabilité [1938b].- W. Doeblin, Étude de l’ensemble de puissances d’une loi de probabilité [1938c].- W. Doeblin, Sur les sommes d’un grand nombre de vecteurs aléatoires [1938d].- W. Doeblin, Sur un problème de calcul des probabilités [1939b].- W. Doeblin, Sur les sommes d’un grand nombre de variables aléatoires indépendantes [1939c].- W. Doeblin, Sur l’ensemble de puissances d’une loi de probabilité (1940) [1940f].- W. Doeblin (with remarks by B. Bru and E. Seneta), Sur l’ensemble de puissances d’une loi de probabilité [1946].- Part IV Chapman’s Equations. Part IV.1 Documents Published Before the pli cacheté: W. Doeblin (with a remark by B. Bru), Sur certaines mouvements aléatoires discontinus [1939d].- W. Doeblin, Sur l’équation de Kolmogoroff [1938h].- W. Doeblin, Sur certains mouvements aléatoires [1939a].- W. Doeblin, Sur l’équation de Kolmogoroff [1940b].- W. Doeblin, Sur des mouvements mixtes [1940c].- Part IV.2 The pli cacheté: M. Yor, Présentation du pli cacheté.- W. Doeblin (with remarks by Bernard Bru and Marc Yor), Sur l’équation de Kolmogoroff, pli cacheté déposé le 26 février 1940, ouvert le 18 mai 2000 [1940g/2000].- B. Bru, Notes de lecture du pli cacheté.- W. Doeblin (with remarks by Bernard Bru), Exposé(s) sur l’équation de Chapman [1938i/2000].- Part IV.3 Archival Documents Related to the pli cacheté: B. Bru, Introduction to Doeblin’s “Sur la solution de M. Hostinský de l’équation de Chapman”.- W. Doeblin, Sur la solution de M. Hostinský de l’équation de Chapman [1940h/1993].- W.Doeblin (with an introduction by B. Bru and E. Seneta), Le cahier jaune: Recherche sur l’équation de Chapman. Propriétés communes aux mouvements régis par l’équation de Chapman [1940i/2020].- Part V Appendix: B. Bru and E. Seneta, Postface.- Acknowledgements.- Credits.- Bibliography.- Supplementary Reading.
£71.24
Springer International Publishing AG Design and Analysis of Experiments
Book SynopsisThis book offers a step-by-step guide to the experimental planning process and the ensuing analysis of normally distributed data, emphasizing the practical considerations governing the design of an experiment. Data sets are taken from real experiments and sample SAS programs are included with each chapter. Experimental design is an essential part of investigation and discovery in science; this book will serve as a modern and comprehensive reference to the subject.Trade Review“The textbook provides a practically oriented version of design and analysis of experiments. The corresponding methods are illustrated by means of numerous simple experiments. Thus, the models and methods are equipped with many examples, exercises, numerical results and related tables and figures. ... The present volume can be recommended as textbook for lectures on models and methods of experimental design as well as handbook for use in practice.” (Kurt Marti, zbMATH 1383.62001, 2018)Table of ContentsPrinciples and Techniques.- Planning Experiments.- Designs With One Source of Variation.- Inferences for Contrasts and Treatment Means.- Checking Model Assumptions.- Experiments With Two Crossed Treatment Factors.- Several Crossed Treatment Factors.- Polynomial Regression.- Analysis of Covariance.- Complete Block Designs.- Incomplete Block Designs.- Designs With Two Blocking Factors.- Confounded Two-Level Factorial Experiments.- Confounding in General Factorial Experiments.- Fractional Factorial Experiments.- Response Surface Methodology.- Random Effects and Variance Components.- Nested Models.- Split-Plot Designs
£104.49
Springer International Publishing AG New Advances in Statistics and Data Science
Book SynopsisThis book is comprised of the presentations delivered at the 25th ICSA Applied Statistics Symposium held at the Hyatt Regency Atlanta, on June 12-15, 2016. This symposium attracted more than 700 statisticians and data scientists working in academia, government, and industry from all over the world. The theme of this conference was the “Challenge of Big Data and Applications of Statistics,” in recognition of the advent of big data era, and the symposium offered opportunities for learning, receiving inspirations from old research ideas and for developing new ones, and for promoting further research collaborations in the data sciences. The invited contributions addressed rich topics closely related to big data analysis in the data sciences, reflecting recent advances and major challenges in statistics, business statistics, and biostatistics. Subsequently, the six editors selected 19 high-quality presentations and invited the speakers to prepare full chapters for this book, which showcases new methods in statistics and data sciences, emerging theories, and case applications from statistics, data science and interdisciplinary fields. The topics covered in the book are timely and have great impact on data sciences, identifying important directions for future research, promoting advanced statistical methods in big data science, and facilitating future collaborations across disciplines and between theory and practice.Table of Contents*Under attachments tab*
£71.99
Springer International Publishing AG Discrete Probability Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding
Book SynopsisThe emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.Trade Review“This is a book that any discrete proababilist will want to have on the shelf. It is a comprehensive extension of the author's masterfully written text Markov Chains ... Surprisingly; the book contains an extensive amount of information theory. ... In my opinion the new book would be ideal for a year-long course on discrete probability.” (Yevgeniy Kovchegov, Mathematical Reviews, May, 2018)“This is a very carefully and well-written book. The real pleasure comes from the contents but also from the excellent fonts and layout. Graduate university students and their teachers can benefit a lot of reading and using this book. There are more than good reasons to strongly recommend the book to anybody studying, teaching and/or researching in probability and its applications.” (Jordan M. Stoyanov, zbMATH 1386.60003, 2018) “This book is an excellent piece of writing. It has the strictness of a mathematical book whose traditional purpose is to state and prove theorems, and also has the features of a book on an engineering topic, where solved and unsolved exercises are provided. I appreciated the very carefully selected solved examples that are interwoven in each chapter. They provide an indispensable aid to digest the concepts and methods presented.” (Dimitrios Katsaros, Computing Reviews, February, 21, 2018) “This is a comprehensive volume on the application of discrete probability to combinatorics, information theory, and related fields. It is accessible for first-year graduate students. … Results are easy to find and reasonably easy to understand. … Summing Up: Recommended. Graduate students and faculty.” (M. Bona, Choice, Vol. 54 (12), August, 2017)Table of ContentsIntroduction.- 1.Events and probability.- 2.Random variables.- 3.Bounds and inequalities.- 4.Almost-sure convergence.- 5.Coupling and the variation distance.- 6.The probabilistic method.- 7.Codes and trees.- 8.Markov chains.- 9.Branching trees.- 10.Markov fields on graphs.- 11.Random graphs.- 12.Recurrence of Markov chains.- 13.Random walks on graphs.- 14.Asymptotic behaviour of Markov chains.- 15.Monte Carlo sampling.- 16. Convergence rates.- Appendix.- Bibliography.
£62.99
Springer International Publishing AG Practical Tools for Designing and Weighting
Book SynopsisThe goal of this book is to put an array of tools at the fingertips of students, practitioners, and researchers by explaining approaches long used by survey statisticians, illustrating how existing software can be used to solve survey problems, and developing some specialized software where needed. This volume serves at least three audiences: (1) students of applied sampling techniques; 2) practicing survey statisticians applying concepts learned in theoretical or applied sampling courses; and (3) social scientists and other survey practitioners who design, select, and weight survey samples. The text thoroughly covers fundamental aspects of survey sampling, such as sample size calculation (with examples for both single- and multi-stage sample design) and weight computation, accompanied by software examples to facilitate implementation. Features include step-by-step instructions for calculating survey weights, extensive real-world examples and applications, and representative programming code in R, SAS, and other packages. Since the publication of the first edition in 2013, there have been important developments in making inferences from nonprobability samples, in address-based sampling (ABS), and in the application of machine learning techniques for survey estimation. New to this revised and expanded edition: • Details on new functions in the PracTools package • Additional machine learning methods to form weighting classes • New coverage of nonlinear optimization algorithms for sample allocation • Reflecting effects of multiple weighting steps (nonresponse and calibration) on standard errors • A new chapter on nonprobability sampling • Additional examples, exercises, and updated references throughout Richard Valliant, PhD, is Research Professor Emeritus at the Institute for Social Research at the University of Michigan and at the Joint Program in Survey Methodology at the University of Maryland. He is a Fellow of the American Statistical Association, an elected member of the International Statistical Institute, and has been an Associate Editor of the Journal of the American Statistical Association, Journal of Official Statistics, and Survey Methodology. Jill A. Dever, PhD, is Senior Research Statistician at RTI International in Washington, DC. She is a Fellow of the American Statistical Association, Associate Editor for Survey Methodology and the Journal of Official Statistics, and an Assistant Research Professor in the Joint Program in Survey Methodology at the University of Maryland. She has served on several panels for the National Academy of Sciences and as a task force member for the American Association of Public Opinion Research’s report on nonprobability sampling. Frauke Kreuter, PhD, is Professor and Director of the Joint Program in Survey Methodology at the University of Maryland, Professor of Statistics and Methodology at the University of Mannheim, and Head of the Statistical Methods Research Department at the Institute for Employment Research (IAB) in Nürnberg, Germany. She is a Fellow of the American Statistical Association and has been Associate Editor of the Journal of the Royal Statistical Society, Journal of Official Statistics, Sociological Methods and Research, Survey Research Methods, Public Opinion Quarterly, American Sociological Review, and the Stata Journal. She is founder of the International Program for Survey and Data Science and co-founder of the Coleridge Initiative.Trade Review“This book attempts to explain long used approaches, illustrate how existing software can be used to solve survey problems, and develop some specialized software where needed with a focus on related practitioners (i.e. students, survey statisticians, and other survey practitioners). … this book may be useful to students, survey statisticians, social scientists and other survey practitioners. The book may also serve as a useful reference for other professionals engaged in the conduct of sample surveys.” (Sada Nand Dwivedi, ISCB News, iscb.info, Issue 67, June, 2019)Table of ContentsPrefaceAcknowledgements1 An Overview of Sample Design and Weighting1.1 Background and Terminology1.2 Chapter GuidePart I Designing Single-Stage Sample Surveys2 Project 1: Design a Single-Stage Personnel Survey2.1 Specifications for the Study2.2 Questions Posed by the Design Team2.3 Preliminary Analyses2.4 Documentation2.5 Next Steps3 Sample Design and Sample Size for Single-Stage Surveys 3.1 Determining a Sample Size for a Single-Stage Design 3.1.1 Simple Random Sampling3.1.2 Stratified Simple Random Sampling3.2 Finding Sample Sizes When Sampling with Varying Probabilities 3.2.1 Probability Proportional to Size Sampling3.2.2 Regression Estimates of Totals3.3 Other Methods of Sampling3.4 Estimating Population Parameters from a Sample3.5 Special Topics3.5.1 Rare Characteristics3.5.2 Domain Estimates3.6 More Discussion of Design Effects3.7 Software for Sample Selection3.7.1 R Packages3.7.2 SAS PROC SURVEYSELECTExercises4 Power Calculations and Sample Size Determination 4.1 Terminology and One-Sample Tests4.2 Power in a One-Sample Test4.3 Two-Sample Tests4.3.1 Differences in Means4.3.2 Differences in Proportions4.3.3 Special Case: Relative Risk4.3.4 Special Case: Effect Sizes4.4 R Power Functions4.5 Power and Sample Size Calculations in SAS. Exercises5 Mathematical Programming5.1 Multicriteria Optimization5.2 Microsoft Excel Solver5.3 SAS PROC NLP5.4 SAS PROC OPTMODEL5.5 R Alabama Package<6 Outcome Rates and Effect on Sample Size6.1 Disposition Codes6.2 Definitions of Outcome Rates6.3 Sample Units with Unknown AAPOR Classification6.4 Weighted Versus Unweighted Rates6.5 Accounting for Sample Losses in Determining Initial Sample Size6.5.1 Sample Size Inflation Rates at Work6.5.2 ReplicatesExercises7 The Personnel Survey Design Project: One Solution 7.1 Overview of the Project 7.2 Formulate the Optimization Problem7.2.1 Objective Function 7.2.2 Decision Variables 7.2.3 Optimization Parameters7.2.4 Specified Survey Constraints 7.3 One Solution 7.3.1 Power Analyses7.3.2 Optimization Results7.4 Additional Sensitivity Analysis7.5 Conclusion Part II Multistage Designs 8 Project 2: Designing an Area Sample 9 Designing Multistage Samples 9.1 Types of PSUs 9.2 Basic Variance Results 9.2.1 Two-Stage Sampling 9.2.2 Nonlinear Estimators in Two-Stage Sampling 9.2.3 More General Two-Stage Designs 9.2.4 Three-Stage Sampling 9.3 Cost Functions and Optimal Allocations for Multistage Sampling 9.3.1 Two-Stage Sampling When Numbers of Sample PSUs and Elements per PSU Are Adjustable 9.3.2 Three-Stage Sampling When Sample Sizes Are Adjustable 9.3.3 Two- and Three-Stage Sampling with a Fixed Set of PSUs 9.4 Estimating Measures of Homogeneity and Variance Components9.4.1 Two-Stage Sampling 9.4.2 Three-Stage Sampling 9.4.3 Using Anticipated Variances The lme4 R package has been updated so that the syntax in the 1st edition no longer works. We will revise the examples in this section for the new version of the package.9.5 Stratification of PSUs 9.6 Identifying Certainties Exercises10 Area Sampling10.1 Census Geographic Units10.2 Census Data and American Community Survey Data10.3 Units at Different Stages of Sampling10.3.1 Primary Sampling Units10.3.2 Secondary Sampling Units10.3.3 Ultimate Sampling Units10.4 Examples of Area Probability Samples10.4.1 Current Population Survey10.4.2 National Survey on Drug Use and Health10.4.3 Panel Arbeitsmarkt und Soziale Sicherung10.5 Composite MOS for Areas10.5.1 Designing the Sample from Scratch10.5.2 Using the Composite MOS with an Existing PSU Sample10.6 Effects of Population Change: The New Construction Issue10.7 Special Address Lists10.7.1 Allocations in ABS using Mathematical Programming Mathematical programming allows efficient allocations to be made to domains (e.g., age groups) using information on housing units that can be purchased from commercial list makers. Discussion and examples will be added to illustrate this technique. The following article will be the basis for examples:Valliant, R., Hubbard, F., Lee, S., Chang, W. (2014). “Efficient Use of Commercial Lists in Household Sampling”, Journal of Survey Statistics and Methodology, 2, 182-209.Exercises11 The Area Sample Design: One SolutionPart III Survey Weights and Analyses12 Project 3: Weighting a Personnel Survey13 Basic Steps in Weighting13.1 Overview of Weighting13.2 Theory of Weighting and Estimation13.3 Base Weights13.4 Adjustments for Unknown Eligibility13.5 Adjustments for Nonresponse13.5.1 Weighting Class Adjustments13.5.2 Propensity Score Adjustments13.5.3 Classification Algorithms13.6 Collapsing Predefined Classes13.7 Weighting for Multistage Designs13.8 Next Steps in WeightingExercises14 Calibration and Other Uses of Auxiliary Data in Weighting14.1 Weight Calibration14.2 Poststratified and Raking Estimators14.3 GREG and Calibration Estimation14.3.1 Links Between Models, Sample Designs, and Estimators-Special Cases14.3.2 More General Examples14.4 Weight Variability14.4.1 Quantifying the Variability14.4.2 Methods to Limit VariabilityExercises15 Variance Estimation15.1 Exact Methods15.2 Linear Versus Nonlinear Estimators15.3 Linearization Variance Estimation15.3.1 Estimation Method15.3.2 Confidence Intervals and Degrees of Freedom15.3.3 Accounting for Non-negligible Sampling Fractions15.3.4 Domain Estimation15.3.5 Assumptions and Limitations15.3.6 Special Cases: Poststratification and Quantiles15.3.7 Handling Multiple Weighting Steps with Linearization15.4 Replication15.4.1 Jackknife Replication15.4.2 Balanced Repeated Replication15.4.3 Bootstrap15.5 Combining PSUs or Strata15.5.1 Combining to Reduce the Number of Replicates15.5.2 How Many Groups and Which Strata and PSUs to Combine15.5.3 Combining Strata in One-PSU-per-Stratum Designs15.6 Handling Certainty PSUsExercises 16 Weighting the Personnel Survey: One Solution16.1 The Data Files16.2 Base Weights16.3 Disposition Codes and Mapping into Weighting Categories16.4 Adjustment for Unknown Eligibility16.5 Variables Available for Nonresponse Adjustment16.6 Nonresponse Adjustments16.7 Calibration to Population Counts16.8 Writing Output Files16.9 Example TabulationsPart IV Other Topics17 Multiphase Designs17.1 What is a Multiphase Design?17.2 Examples of Different Multiphase Designs17.2.1 Double Sampling for Stratification17.2.2 Nonrespondent Subsampling17.2.3 Responsive Designs17.2.4 General Multiphase Designs17.3 Survey Weights17.3.1 Base Weights17.3.2 Analysis Weights17.4 Estimation17.4.1 Descriptive Point Estimation17.4.2 Variance Estimation17.4.3 Generalized Regression Estimator (GREG)17.5 Design Choices 17.5.1 Multiphase versus Single Phase 17.5.2 Sample Size Calculations17.6 R SoftwareExercises18. Non-probability Samples18.1 Types of Non-probability Samples18.2 Potential Problems18.3 Quasi-randomization Approach18.4 Superpopulation Modeling Approach19 Process Control and Quality Measures19.1 Design and Planning19.2 Quality Control in Frame Creation and Sample Selection19.3 Monitoring Data Collection . . .19.4 Performance Rates and Indicators19.5 Data Editing19.5.1 Editing Disposition Codes19.5.2 Editing the Weighting Variables19.6 Quality Control of Weighting Steps19.7 Specification Writing and Programming19.8 Project Documentation and Archiving Part V. Backmatter Appendix A: Notation GlossaryAppendix B: Data SetsAppendix C: R Functions Used in this Book1 r="" overviewC.2 Author-Defined R FunctionsReferencesSolutions to Selected ExercisesSubject Index
£104.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Teubner-Taschenbuch der Stochastik:
Book SynopsisDieses umfassende Lehr-und Nachschlagewerk für Naturwissenschaftler und Ingenieure vermittelt dem Leser zentrale Teile der Wahrscheinlichkeitstheorie, der Theorie stochastischer Prozesse sowie der mathematischen Statistik.Table of Contents0 Einführung.- 1 Wahrscheinlichkeitstheorie.- 1.1 Zufällige Ereignisse.- 1.2 Wahrscheinlichkeit zufälliger Ereignisse.- 1.3 Bedingte Wahrscheinlichkeit und Unabhängigkeit.- 1.4 Diskrete Zufallsgrößen.- 1.4.1 Grundlagen.- 1.4.2 Parametrische Kenngrößen.- 1.4.3 Diskrete Wahrscheinlichkeitsverteilungen.- 1.4.4 Momenterzeugende Funktionen.- 1.5 Stetige Zufallsgrößen.- 1.5.1 Grundlagen.- 1.5.2 Parametrische Kenngrößen.- 1.5.3 Nichtnegative Zufallsgrößen.- 1.5.4 Stetige Wahrscheinlichkeitsverteilungen.- 1.5.4.1 Normalverteilung (Gaußsche Verteilung).- 1.5.4.2 Logarithmische Normalverteilung.- 1.5.4.3 Inverse Gaußverteilung.- 1.5.4.4 Weibuliverteilung.- 1.5.4.5 Erlangverteilung.- 1.5.4.6 Gammaverteilung.- 1.5.4.7 Betaverteilung.- 1.5.5 Momenterzeugende Funktionen.- 1.6 Funktionen einer Zufallsgröße.- 1.7 Simulation von Zufallsgrößen.- 1.8 Mehrdimensionale Zufallsgrößen.- 1.8.1 Zweidimensionale Zufallsgrößen.- 1.8.1.1 Gemeinsame Wahrscheinlichkeitsverteilung.- 1.8.1.2 Unabhängige Zufallsgrößen.- 1.8.1.3 Bedingte Verteilung.- 1.8.1.4 Funktionen zweier Zufallsgrößen.- 1.8.1.5 Abhängigkeitsmaße für zwei Zufallsgrößen.- 1.8.1.6 Zweidimensionale Normalverteilung.- 1.8.1.7 Diskrete zweidimensionale Zufallsgrößen.- 1.8.2 n-dimensionale Zufallsgrößen.- 1.8.2.1 Grundlagen.- 1.8.2.2 Summen von Zufallsgrößen.- 1.8.2.3 n-dimensionale Normalverteilung.- 1.9 Ungleichungen in der Wahrscheinlichkeitstheorie.- 1.9.1 Abschätzungen für Wahrscheinlichkeiten.- 1.9.1.1 Ungleichungen vom Markov-Tschebyschev-Typ.- 1.9.1.2 Exponentialabschätzungen.- 1.9.1.3 Ungleichungen fur Maxima von Summen.- 1.9.2 Ungleichungen und Abschätzungen für Momente.- 1.10 Grenzwertsätze in der Wahrscheinlichkeitstheorie.- 1.10.1 Konvergenzarten.- 1.10.2 Gesetze der großen Zahlen.- 1.10.2.1 Schwache Gesetze der großen Zahlen.- 1.10.2.2 Starke Gesetze der großen Zahlen.- 1.10.3 Zentraler Grenzwertsatz.- 1.10.4 Lokale Grenzwertsätze.- 1.11 Charakteristische Funktionen.- 1.11.1 Komplexe Zufallsgrößen.- 1.11.2 Eigenschaften charakteristischer Funktionen.- 1.11.3 Charakteristische Funktion diskreter Zufallsgrößen.- 2 Stochastische Prozesse.- 2.1 Einführung.- 2.2 Kenngrößen stochastischer Prozesse.- 2.3 Eigenschaften stochastischer Prozesse.- 2.4 Spezielle stochastische Prozesse.- 2.4.1 Stochastische Prozesse mit stetiger Zeit.- 2.4.2 Stochastische Prozesse mit diskreter Zeit.- 2.5 Poissonsche Prozesse.- 2.5.1 Homogener Poissonprozess.- 2.5.1.1 Definition und Eigenschaften.- 2.5.1.2 Homogener Poissonprozess und Gleichverteilung.- 2.5.2 Inhomogener Poissonprozess.- 2.6 Erneuerungsprozesse.- 2.6.1 Grundlagen.- 2.6.2 Erneuerungsfunktion.- 2.6.2.1 Erneuerungsgleichungen.- 2.6.2.2 Abschätzungen der Erneuerungsfunktion.- 2.6.3 Rekurrenzzeiten.- 2.6.4 Asymptotisches Verhalten.- 2.6.5 Stationäre Erneuerungsprozesse.- 2.6.6 Alternierende Erneuerungsprozesse.- 2.6.7 Kumulative stochastische Prozesse.- 2.6.8 Regenerative stochastische Prozesse.- 2.7 Markovsche Ketten mit diskreter Zeit.- 2.7.1 Grundlagen und Beispiele.- 2.7.2 Klassifikation der Zustände.- 2.7.2.1 Abgeschlossene Zustandsmengen.- 2.7.2.2 Äquivalenzklassen.- 2.7.2.3 Periodizität.- 2.7.2.4 Rekurrenz und Transienz.- 2.7.3 Grenzwertsätze und stationäre Verteilung.- 2.7.4 Geburts- und Todesprozesse.- 2.8 Markovsche Ketten mit stetiger Zeit.- 2.8.1 Grundlagen.- 2.8.2 Kolmogorovsche Gleichungen.- 2.8.3 Stationäre Zustandswahrscheinlichkeiten.- 2.8.4 Konstruktion Markovscher Systeme.- 2.8.5 Erlangsche Phasenmethode.- 2.8.6 Geburts- und Todesprozesse.- 2.8.6.1 Zeitabhängige Zustandswahrscheinlichkeiten.- 2.8.6.2 Stationäre Zustandswahrscheinlichkeiten.- 2.8.6.3 Verweildauern.- 2.8.7 Semi-Markovsche Prozesse.- 2.9 Martingale.- 2.9.1 Martingale in diskreter Zeit.- 2.9.2 Martingale in stetiger Zeit.- 2.10 Wiener Prozess.- 2.10.1 Definition und Eigenschaften.- 2.10.2 Niveauüberschreitung.- 2.10.3 Transformationen des Wiener Prozesses.- 2.10.3.1 Elementare Transformationen.- 2.10.3.2 Ornstein-Uhlenbeck-Prozess.- 2.10.3.3 Wiener Prozess mit Drift.- 2.10.3.4 Integraltransformationen.- 2.11 Spektralanalyse stationärer Prozesse.- 2.11.1 Grundbegriffe.- 2.11.2 Prozesse mit diskretem Spektrum.- 2.11.3 Prozesse mit stetigem Spektrum.- 2.11.3.1 Spektralzerlegung der Kovarianzfunktion.- 2.11.3.2 Spektralzerlegung des Prozesses.- 3 Mathematische Statistik.- 3.1 Stichproben und ihre empirische Auswertung.- 3.1.1 Stichproben.- 3.1.2 Häufigkeits- und Summenhäufigkeitsverteilung.- 3.1.3 Empirische Punktschätzung.- 3.1.3.1 Mittelwertsmaße.- 3.1.3.2 Streuungsmaße.- 3.1.4 Graphische Anpassung einer empirischen Verteilung an eine theoretische Verteilung.- 3.2 Punktschätzung.- 3.2.1 Eigenschaften von Schätzfunktionen.- 3.2.2 Schätzmethoden.- 3.2.2.1 Maximum-Likelihood-Methode.- 3.2.2.2 Momentenmethode.- 3.2.3 Wahrscheinlichkeitsverteilungen von Schätzfunktionen.- 3.2.3.1 Stichprobenverteilungen.- 3.2.3.2 Extremwertverteilungen.- 3.3 Intervallschätzung.- 3.3.1 Grundlagen.- 3.3.2 Konfidenzintervalle für Parameter der Normalverteilung.- 3.3.2.1 Konfidenzintervall für den Erwartungswert (Varianz bekannt).- 3.3.2.2 Konfidenzintervall für den Erwartungswert (Varianz unbekannt).- 3.3.2.3 Konfidenzintervall für die Varianz.- 3.3.3 Approximative Konfidenzintervalle.- 3.3.3.1 Konfidenzintervall für eine Wahrscheinlichkeit.- 3.3.3.2 Konfidenzintervall für den Erwartungswert einer poissonverteilten Zufallsgröße.- 3.4 Parametertests.- 3.4.1 Grundlagen.- 3.4.2 Tests über Parameter der Normalverteilung.- 3.4.2.1 Test über den Erwartungswert bei bekannter Varianz.- 3.4.2.2 Test über den Erwartungswert bei unbekannter Varianz.- 3.4.2.3 t-Test für verbundene Stichproben.- 3.4.2.4 Test auf Gleichheit der Erwartungswerte zweier Zufallsgrößen.- 3.4.2.5 Test auf Gleichheit der Varianzen.- 3.4.3 Approximative Tests.- 3.4.3.1 Test über eine Wahrscheinlichkeit.- 3.4.3.2 Vergleich zweier Wahrscheinlichkeiten.- 3.5 Verteilungsfreie Tests.- 3.5.1 Anpassungstests.- 3.5.1.1 Chi-Quadrat-Anpassungstest.- 3.5.1.2 Kolmogorov-Smirnov-Test.- 3.5.2 Tests auf Homogenität.- 3.5.2.1 Vorzeichentest.- 3.5.2.2 Wilcoxon-Vorzeichen-Rang-Test.- 3.5.2.3 Zwei-Stichproben-Rang-Test von Wilcoxon (-Mann-Whitney).- 3.5.2.4 Zwei-Stichproben-Iterationstest von Wald-Wolfowitz.- 3.5.2.5 Chi-Quadrat-Homogenitätstest.- 3.5.3 Chi-Quadrat-Unabhängigkeitstest.- 3.6 Korrelationsanalyse.- 3.6.1 Einführung.- 3.6.2 Einfacher Korrelationskoeffizient.- 3.6.3 Rangkorrelationskoeffizient von Spearman.- 3.7 Regressionsanalyse.- 3.7.1 Einführung.- 3.7.2 Einfache lineare Regression.- 3.7.2.1 Punktschätzung der Modellparameter.- 3.7.2.2 Konfidenz- und Prognoseintervalle.- 3.7.2.3 Tests über Regressionskoeffizienten und Anpassung.- 3.7.3 Nichtlineare Regressionsfunktion.- 3.7.3.1 Polynomiale Regressionsfunktion.- 3.7.3.2 Exponentielle Regressionsfunktion.- 3.7.4 Mehrfache lineare Regression.- 3.7.4.1 Punktschätzung der Modellparameter.- 3.7.4.2 Tests über Modellparameter.- 3.7.4.3 Konfidenz- und Prognoseintervalle.- 3.7.4.4 Abhängigkeits- und Prognosemaße.- 3.7.4.5 Voraussetzungen und funktionell richtiger Ansatz.- 3.7.4.6 Multikollinearität.- 3.7.4.7 Dominante Beobachtungen, Ausreißer, robuste Regression.- 3.7.4.8 Auswahl der Einflussgrößen.- 3.8 Multivariate Analyseverfahren.- 3.8.1 Grundbegriffe.- 3.8.2 Multivariate Varianzanalyse.- 3.8.2.1 Tests über Vektoren von Erwartungswerten.- 3.8.2.2 Das multivariate lineare Modell.- 3.8.2.3 Tests über Varianzstrukturen.- 3.8.3 Hauptkomponenten- und Faktoranalyse.- 3.8.3.1 Hauptkomponentenanalysen.- 3.8.3.2 Faktoranalyse.- 3.8.4 Diskrimination und Klassifikation.- 3.8.5 Clusteranalyse.- 3.8.5.1 Punktwolken und Distanzwahl.- 3.8.5.2 Zielfunktionen und Verfahrenstypen.- 3.8.5.3 Dendrogramme.- 3.8.6 Multidimensionale Skalierung.- 3.9 Statistische Versuchsplanung.- 3.9.1 Einführung.- 3.9.2 Optimale Versuchspläne.- 3.9.3 Faktorielle Versuchspläne.- 3.9.3.1 Grundlagen.- 3.9.3.2 Vollständige zweistufige faktorielle Versuchspläne.- 3.9.3.3 Teilweise zweistufige faktorielle Versuchspläne.- 3.9.3.4 Blockbildung in faktoriellen Versuchsplänen.- 3.9.3.5 Ergebnisverbesserung vermittels der Methode von Box-Wilson.- 3.10 Statistische Methoden in der Prozesskontrolle.- 3.10.1 Grundlagen.- 3.10.2 Shewart-Kontrollkarten.- 3.10.2.1 ?X- und R- Kontrollkarten.- 3.10.2.2 Kontrollkarten für Einzelmessungen.- 3.10.2.3 Kontrollkarten für die Gut-Schlecht-Prüfung.- 3.10.3 CUSUM-Kontrollkarten.- 3.10.4 EWMA-Kontrollkarten.- Tafeln.- Tafel I Verteilungsfunktion der standardisierten Normalverteilung.- Tafel III Quantile der Chi-Quadrat-Verteilung.- Tafel V Quantile der Testfunktion für den Kolmogorov-Smirnov-Test.- Tafel VIa Kritische Werte für den Zwei-Stichproben-Rang-Test von Wilcoxon (? = 0,01).- Tafel VIb Kritische Werte für den Zwei-Stichproben-Rang-Test von Wilcoxon (? = 0,05).- Tafel VII Kritische Werte für den Zwei-Stichproben-Iterationstest.- Tafel VIII Faktoren für die Konstruktion von Kontrollkarten.- Tafel IX Diskrete Wahrscheinlichkeitsverteilungen.- Tafel X Stetige Wahrscheinlichkeitsverteilungen.- Tafel XI Konfidenzintervalle.- Tafel XII Parametertests.- Literatur.
£28.49
Springer Fachmedien Wiesbaden Teubner-Taschenbuch der statistischen Physik
Book SynopsisAus moderner Sicht werden in diesem Teubner-Taschenbuch die Grundlagen und wichtige Anwendungen der statistischen Physik dargestellt. Auf eine gründliche Darstellung der Begriffsbildungen der statistischen Physik, auf die korrekte Herleitung grundlegender Gleichungen und auf die Durchführung wichtiger Beweise wird besonderer Wert gelegt. Das Buch eignet sich als Begleittext für Kurs- und Spezialvorlesungen, als Repetitorium zur Prüfungsvorbereitung und als Nachschlagewerk zur raschen Information für breite Leserkreise aus Mathematik, Naturwissenschaften und technischen Disziplinen, insbesondere für Studenten dieser Fachrichtungen.Table of ContentsKombinatorik - Wahrscheinlichkeitstheorie - Quantenmechanik und Wahrscheinlichkeit - Thermodynamik - Statistische Physik der Gleichgewichtssysteme - Statistische Physik der Systeme im Nichtgleichgewicht - Statistische Physik und Informationstheorie - Phasenraummethoden der Quantenstatistik - Fraktaltheorie und Perkolationstheorie - Theorie dynamischer Systeme, Chaostheorie, Ergodentheorie - Statistische Thermodynamik chemischer Systeme - Statistische Theorie biologischer Systeme - Synergetik, weitere Anwendungen der statistischen Physik
£49.49
Springer Fachmedien Wiesbaden Wahrscheinlichkeitsrechnung
Book SynopsisTable of Contents1. Grundbegriffe.- 2. Elementare Kombinatorik.- 3. Wahrscheinlichkeitsfunktionen und ihre Eigenschaften.- 4. Unabhängigkeit von Ereignissen und Versuchen.- 5. Die Begriffe Zufallsvariable, Wahrscheinlichkeitsdichte, Wahrscheinlichkeitsverteilungsfunktionen, Erwartungswert, Varianz, Standardabweichung.- 6. Das schwache Gesetz der großen Zahlen.- 2. Lösungen ausgewählter Aufgaben.
£40.84
Springer Fachmedien Wiesbaden Wahrscheinlichkeitstheorie und Statistik:
Book SynopsisAufbauend auf einer ausführlichen Darstellung der wahrscheinlichkeitstheoretischen Grundbegriffe und deren Anwendungen werden die Gesetze der großen Zahlen und der zentrale Grenzwertsatz behandelt, gefolgt von einer Darstellung der statistischen Modellbildung, der Schätztheorie und der Testtheorie. Ziel des Buches ist es, den mit den Grundlagen der Mathematik vertrauten Leser in die Methoden der Wahrscheinlichkeitstheorie und Statistik so einzuführen, dass dieser ein verlässliches Fundament an Kenntnissen erwirbt, sowohl für die Anwendung dieser Methoden bei praktischen Problemen als auch für weiterführende Studien.Trade ReviewZur 2. Auflage: "Eine überaus gut gelungene Darstellung." ekz-Informationsdienst, ID 42/05 Zur 1. Auflage: "Empfehlenswert für Studierende der Mathematik und solcher Fächer, die Stochastik verwenden." ekz-bibl. Bereich, 14.09.01Table of ContentsWahrscheinlichkeitsraum - Zufallsvariable - Erwartungswert - Stochastische Unabhängigkeit - Gesetze der großen Zahlen - Zentraler Grenzwertsatz - Markov-Ketten - Statistisches Experiment - Entscheidungstheorie - Schätztheorie - Lineares Modell - Testtheorie
£28.49
Springer Fachmedien Wiesbaden Baufachrechnen: Grundlagen Hochbau — Tiefbau —
Book SynopsisMit zahlreichen Aufgaben und technischen Zeichnungen vermittelt das Buch praxisnah und nach bewährtem Prinzip die mathematischen Grundlagen für alle Bauberufe. Table of ContentsGrundrechenarten - Längen und Flächen - Körper - Physikalische Größen - Baustoffbedarf
£36.09
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Improved Bonferroni Inequalities via Abstract
Book SynopsisThis introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Möbius functions.Table of Contents1. Introduction and Overview.- 2. Preliminaries.- 3.Bonferroni Inequalities via Abstract Tubes.- 4. Abstract Tubes via Closure and Kernel Operators.- 5. Recursive Schemes.- 6. Reliability Applications.- 7. Combinatorial Applications and Related Topics.- Bibliography.- Index.
£31.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG An Introduction to Infinite-Dimensional Analysis
Book SynopsisBased on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.Trade ReviewFrom the reviews: "This is an extended version of the author’s ‘An introduction to infinite-dimensional analysis’ published by Scuola Normale Superiore, Pisa … . A well written textbook (even an introductory research monograph), suitable for teaching a graduate course." (Neils Jacob, Zentralblatt MATH, Vol. 1109 (11), 2007) "The present volume collects together … the notes of the course on infinite-dimensional analysis held by the author at the Scuola Normale Superiore of Pisa in recent years. The book is intended for people who have some knowledge of functional analysis … . It provides an extremely useful tool for those scholars who are interested in learning some basics about Gaussian measures in Hilbert spaces, Brownian motion, Markov transition semigroups … . The book is well written and all arguments are clearly and rigorously presented." (Sandra Cerrai, Mathematical Reviews, Issue 2009 a)Table of ContentsGaussian measures in Hilbert spaces.- The Cameron–Martin formula.- Brownian motion.- Stochastic perturbations of a dynamical system.- Invariant measures for Markov semigroups.- Weak convergence of measures.- Existence and uniqueness of invariant measures.- Examples of Markov semigroups.- L2 spaces with respect to a Gaussian measure.- Sobolev spaces for a Gaussian measure.- Gradient systems.
£44.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Fokker-Planck Equation: Methods of Solution and Applications
Book SynopsisThis is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.Table of Contents1. Introduction.- 1.1 Brownian Motion.- 1.1.1 Deterministic Differential Equation.- 1.1.2 Stochastic Differential Equation.- 1.1.3 Equation of Motion for the Distribution Function.- 1.2 Fokker-Planck Equation.- 1.2.1 Fokker-Planck Equation for One Variable.- 1.2.2 Fokker-Planck Equation for N Variables.- 1.2.3 How Does a Fokker-Planck Equation Arise?.- 1.2.4 Purpose of the Fokker-Planck Equation.- 1.2.5 Solutions of the Fokker-Planck Equation.- 1.2.6 Kramers and Smoluchowski Equations.- 1.2.7 Generalizations of the Fokker-Planck Equation.- 1.3 Boltzmann Equation.- 1.4 Master Equation.- 2. Probability Theory.- 2.1 Random Variable and Probability Density.- 2.2 Characteristic Function and Cumulants.- 2.3 Generalization to Several Random Variables.- 2.3.1 Conditional Probability Density.- 2.3.2 Cross Correlation.- 2.3.3 Gaussian Distribution.- 2.4 Time-Dependent Random Variables.- 2.4.1 Classification of Stochastic Processes.- 2.4.2 Chapman-Kolmogorov Equation.- 2.4.3 Wiener-Khintchine Theorem.- 2.5 Several Time-Dependent Random Variables.- 3. Langevin Equations.- 3.1 Langevin Equation for Brownian Motion.- 3.1.1 Mean-Squared Displacement.- 3.1.2 Three-Dimensional Case.- 3.1.3 Calculation of the Stationary Velocity Distribution Function.- 3.2 Ornstein-Uhlenbeck Process.- 3.2.1 Calculation of Moments.- 3.2.2 Correlation Function.- 3.2.3 Solution by Fourier Transformation.- 3.3 Nonlinear Langevin Equation, One Variable.- 3.3.1 Example.- 3.3.2 Kramers-Moyal Expansion Coefficients.- 3.3.3 Itô’s and Stratonovich’s Definitions.- 3.4 Nonlinear Langevin Equations, Several Variables.- 3.4.1 Determination of the Langevin Equation from Drift and Diffusion Coefficients.- 3.4.2 Transformation of Variables.- 3.4.3 How to Obtain Drift and Diffusion Coefficients for Systems.- 3.5 Markov Property.- 3.6 Solutions of the Langevin Equation by Computer Simulation.- 4. Fokker-Planck Equation.- 4.1 Kramers-Moyal Forward Expansion.- 4.1.1 Formal Solution.- 4.2 Kramers-Moyal Backward Expansion.- 4.2.1 Formal Solution.- 4.2.2 Equivalence of the Solutions of the Forward and Backward Equations.- 4.3 Pawula Theorem.- 4.4 Fokker-Planck Equation for One Variable.- 4.4.1 Transition Probability Density for Small Times.- 4.4.2 Path Integral Solutions.- 4.5 Generation and Recombination Processes.- 4.6 Application of Truncated Kramers-Moyal Expansions.- 4.7 Fokker-Planck Equation for N Variables.- 4.7.1 Probability Current.- 4.7.2 Joint Probability Distribution.- 4.7.3 Transition Probability Density for Small Times.- 4.8 Examples for Fokker-Planck Equations with Several Variables.- 4.8.1 Three-Dimensional Brownian Motion without Position Variable.- 4.8.2 One-Dimensional Brownian Motion in a Potential.- 4.8.3 Three-Dimensional Brownian Motion in an External Force.- 4.8.4 Brownian Motion of Two Interacting Particles in an External Potential.- 4.9 Transformation of Variables.- 4.10 Covariant Form of the Fokker-Planck Equation.- 5. Fokker-Planck Equation for One Variable; Methods of Solution.- 5.1 Normalization.- 5.2 Stationary Solution.- 5.3 Ornstein-Uhlenbeck Process.- 5.4 Eigenfunction Expansion.- 5.5 Examples.- 5.5.1 Parabolic Potential.- 5.5.2 Inverted Parabolic Potential.- 5.5.3 Infinite Square Well for the Schrüdinger Potential.- 5.5.4 V-Shaped Potential for the Fokker-Planck Equation.- 5.6 Jump Conditions.- 5.7 A Bistable Model Potential.- 5.8 Eigenfunctions and Eigenvalues of Inverted Potentials.- 5.9 Approximate and Numerical Methods for Determining Eigenvalues and Eigenfunctions.- 5.9.1 Variational Method.- 5.9.2 Numerical Integration.- 5.9.3 Expansion into a Complete Set.- 5.10 Diffusion Over a Barrier.- 5.10.1 Kramers’ Escape Rate.- 5.10.2 Bistable and Metastable Potential.- 6. Fokker-Planck Equation for Several Variables; Methods of Solution.- 6.1 Approach of the Solutions to a Limit Solution.- 6.2 Expansion into a Biorthogonal Set.- 6.3 Transformation of the Fokker-Planck Operator, Eigenfunction Expansions.- 6.4 Detailed Balance.- 6.5 Ornstein-Uhlenbeck Process.- 6.6 Further Methods for Solving the Fokker-Planck Equation.- 6.6.1 Transformation of Variables.- 6.6.2 Variational Method.- 6.6.3 Reduction to an Hermitian Problem.- 6.6.4 Numerical Integration.- 6.6.5 Expansion into Complete Sets.- 6.6.6 Matrix Continued-Fraction Method.- 6.6.7 WKB Method.- 7. Linear Response and Correlation Functions.- 7.1 Linear Response Function.- 7.2 Correlation Functions.- 7.3 Susceptibility.- 8. Reduction of the Number of Variables.- 8.1 First-Passage Time Problems.- 8.2 Drift and Diffusion Coefficients Independent of Some Variables.- 8.2.1 Time Integrals of Markovian Variables.- 8.3 Adiabatic Elimination of Fast Variables.- 8.3.1 Linear Process with Respect to the Fast Variable.- 8.3.2 Connection to the Nakajima-Zwanzig Projector Formalism.- 9. Solutions of Tridiagonal Recurrence Relations, Application to Ordinary and Partial Differential Equations.- 9.1 Applications and Forms of Tridiagonal Recurrence Relations.- 9.1.1 Scalar Recurrence Relation.- 9.1.2 Vector Recurrence Relation.- 9.2 Solutions of Scalar Recurrence Relations.- 9.2.1 Stationary Solution.- 9.2.2 Initial Value Problem.- 9.2.3 Eigenvalue Problem.- 9.3 Solutions of Vector Recurrence Relations.- 9.3.1 Initial Value Problem.- 9.3.2 Eigenvalue Problem.- 9.4 Ordinary and Partial Differential Equations with Multiplicative Harmonic Time-Dependent Parameters.- 9.4.1 Ordinary Differential Equations.- 9.4.2 Partial Differential Equations.- 9.5 Methods for Calculating Continued Fractions.- 9.5.1 Ordinary Continued Fractions.- 9.5.2 Matrix Continued Fractions.- 10. Solutions of the Kramers Equation.- 10.1 Forms of the Kramers Equation.- 10.1.1 Normalization of Variables.- 10.1.2 Reversible and Irreversible Operators.- 10.1.3 Transformation of the Operators.- 10.1.4 Expansion into Hermite Functions.- 10.2 Solutions for a Linear Force.- 10.2.1 Transition Probability.- 10.2.2 Eigenvalues and Eigenfunctions.- 10.3 Matrix Continued-Fraction Solutions of the Kramers Equation.- 10.3.1 Initial Value Problem.- 10.3.2 Eigenvalue Problem.- 10.4 Inverse Friction Expansion.- 10.4.1 Inverse Friction Expansion for K0(t), G0,0(t) and L0(t).- 10.4.2 Determination of Eigenvalues and Eigenvectors.- 10.4.3 Expansion for the Green’s Function Gn,m(t).- 10.4.4 Position-Dependent Friction.- 11. Brownian Motion in Periodic Potentials.- 11.1 Applications.- 11.1.1 Pendulum.- 11.1.2 Superionic Conductor.- 11.1.3 Josephson Tunneling Junction.- 11.1.4 Rotation of Dipoles in a Constant Field.- 11.1.5 Phase-Locked Loop.- 11.1.6 Connection to the Sine-Gordon Equation.- 11.2 Normalization of the Langevin and Fokker-Planck Equations.- 11.3 High-Friction Limit.- 11.3.1 Stationary Solution.- 11.3.2 Time-Dependent Solution.- 11.4 Low-Friction Limit.- 11.4.1 Transformation to E and x Variables.- 11.4.2 ‘Ansatz’ for the Stationary Distribution Functions.- 11.4.3 x-Independent Functions.- 11.4.4 x-Dependent Functions.- 11.4.5 Corrected x-Independent Functions and Mobility.- 11.5 Stationary Solutions for Arbitrary Friction.- 11.5.1 Periodicity of the Stationary Distribution Function.- 11.5.2 Matrix Continued-Fraction Method.- 11.5.3 Calculation of the Stationary Distribution Function.- 11.5.4 Alternative Matrix Continued Fraction for the Cosine Potential.- 11.6 Bistability between Running and Locked Solution.- 11.6.1 Solutions Without Noise.- 11.6.2 Solutions With Noise.- 11.6.3 Low-Friction Mobility With Noise.- 11.7 Instationary Solutions.- 11.7.1 Diffusion Constant.- 11.7.2 Transition Probability for Large Times.- 11.8 Susceptibilities.- 11.8.1 Zero-Friction Limit.- 11.9 Eigenvalues and Eigenfunctions.- 11.9.1 Eigenvalues and Eigenfunctions in the Low-Friction Limit.- 12. Statistical Properties of Laser Light.- 12.1 Semiclassical Laser Equations.- 12.1.1 Equations Without Noise.- 12.1.2 Langevin Equation.- 12.1.3 Laser Fokker-Planck Equation.- 12.2 Stationary Solution and Its Expectation Values.- 12.3 Expansion in Eigenmodes.- 12.4 Expansion into a Complete Set; Solution by Matrix Continued Fractions.- 12.4.1 Determination of Eigenvalues.- 12.5 Transient Solution.- 12.5.1 Eigenfunction Method.- 12.5.2 Expansion into a Complete Set.- 12.5.3 Solution for Large Pump Parameters.- 12.6 Photoelectron Counting Distribution.- 12.6.1 Counting Distribution for Short Intervals.- 12.6.2 Expectation Values for Arbitrary Intervals.- Appendices.- A1 Stochastic Differential Equations with Colored Gaussian Noise.- A2 Boltzmann Equation with BGK and SW Collision Operators.- A3 Evaluation of a Matrix Continued Fraction for the Harmonic Oscillator.- A4 Damped Quantum-Mechanical Harmonic Oscillator.- A5 Alternative Derivation of the Fokker-Planck Equation.- A6 Fluctuating Control Parameter.- S. Supplement to the Second Edition.- S.1 Solutions of the Fokker-Planck Equation by Computer Simulation (Sect. 3.6).- S.2 Kramers-Moyal Expansion (Sect. 4.6).- S.3 Example for the Covariant Form of the Fokker-Planck Equation (Sect. 4.10).- S.4 Connection to Supersymmetry and Exact Solutions of the One Variable Fokker-Planck Equation (Chap. 5).- S.5 Nondifferentiability of the Potential for the Weak Noise Expansion (Sects. 6.6 and 6.7).- S.6 Further Applications of Matrix Continued-Fractions (Chap. 9).- S.7 Brownian Motion in a Double-Well Potential (Chaps. 10 and 11).- S.8 Boundary Layer Theory (Sect. 11.4).- S.9 Calculation of Correlation Times (Sect. 7.12).- S.10 Colored Noise (Appendix A1).- S.11 Fokker-Planck Equation with a Non-Positive-Definite Diffusion Matrix and Fokker-Planck Equation with Additional Third-Order-Derivative Terms.- References.
£66.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Introduction to the Statistical Analysis of Categorical Data
Book Synopsisto the Statistical Analysis of Categorical Data With 16 Figures and 121 Tables , Springer Prof. Erling B. Andersen University of Copenhagen Department of Statistics 6 Studiestrrede DK-14SS Copenhagen Denmark ISBN 978-3-540-62399-1 CataJoging-in-Publication Data applied ror Oie Oeutsche Bibliothek - CIP-Einheitsaufnahme Andersen, Erling B. : Introduction to the statistical analysis of categorical data analysis: with 121 tables I Erling B. Andersen. -Berlin; Heidelberg; New York; Bucelona; Buda- pest; Hong Kong; London; Milan; Paris; Santa Clara; Singapore; Tokyo: Springer, 1997 ISBN 978-3-540~2399-1 ISBN 978-3~2-59123-5 (eBook) DOI10. 1007/978-3~2-59123-5 This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any o!her way, and storage in data banks. Ouplication of this publication or parts thereof IS permitted only under the provisions of !he German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under !he German Copyright Law. O Springer-Verlag Berlin Heidelberg 1997 Originally published by Springer-Verlag Berlin Heidelberg New York in 1997 The use of general descriptive names, registered names, trademarks, etc. in this publi- cation does not imply, even in !he absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and !herefore free for general use.Table of ContentsIntroduction: The two-way Table.- Basic Theory: Exponential families; Statistical inference in an exponential family; The binomial distribution; The Poisson distribution; Composite hypotheses; Applications to the multinomial distribution; Log-linear models; The two-way contingency table; The numerical solution of the likelihood equations for the log-linear model.- Three-way contingency tables: Log-linear models; Log-linear hypotheses; Estimation; testing hypotheses; Interpretation of the log-linear parameters; Choice of model; Detection of model deviations.- Multi-dimensional contingency tables: The log-linear-model; Classification and interpretation of log-linear models; Choice of model; Diagnostics; Model search strategies.- Incomplete Tables: Random and structural zeros; Counting th number of degrees of freedom; Validity of the X2-approximation.- The Logit Model: The Logit model; Hypothesis testing in the logit model; Logit models with higher order interactions; The Logit model as a regression model.- Logistic Regression Analysis: The logistic regression model; Estimation in the logistic regression model; Numerical solution of the likelihood equations; Checking the fit of the model; Hypothesis testing; Diagnostics; Predictions; Dummy variables; Polytomous response variables.- Association Models: Symmetry models; Marginal homogeneity; RC-association models; Correspondence analysis.- Appendix: Solutions and output to selected excercises.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Handbook of Financial Time Series
Book SynopsisThe Handbook of Financial Time Series, edited by Andersen, Davis, Kreiss and Mikosch, is an impressive collection of survey articles by many of the leading contributors to the ?eld. These articles are mostly very clearly wr- ten and present a sweep of the literature in a coherent pedagogical manner. The level of most of the contributions is mathematically sophisticated, and I imagine many of these chapters will ?nd their way onto graduate reading lists in courses in ?nancial economics and ?nancial econometrics. In reading through these papers, I found many new insights and presentations even in areas that I know well. The book is divided into ?ve broad sections: GARCH-Modeling, Stoch- tic Volatility Modeling, Continuous Time Processes, Cointegration and Unit Roots, and Special Topics. These correspond generally to classes of stoch- tic processes that are applied in various ?nance contexts. However, there are otherthemesthatcutacrosstheseclasses.Thereareseveralpapersthatca- fully articulate the probabilistic structure of these classes, while others are morefocusedonestimation.Stillothersderivepropertiesofextremesforeach class of processes, and evaluate persistence and the extent of long memory. Papers in many cases examine the stability of the process with tools to check for breaks and jumps. Finally there are applications to options, term str- ture, credit derivatives, risk management, microstructure models and other forecasting settings.Trade ReviewFrom the reviews:“Academic researchers and graduate students in statistics, economics and financial engineering, Industry banking, investments and insurance. … The handbook is clearly written and provides a broad and detailed overview of the major topics within financial time series. … serves as a good reference for the financial time series methods and will be invaluable to many researchers. It also excels in giving very clear and concise description of a number of important methodologies.” (Lasse Koskinen, International Statistical Review, Vol. 78 (1), 2010)Table of ContentsRecent Developments in GARCH Modeling.- An Introduction to Univariate GARCH Models.- Stationarity, Mixing, Distributional Properties and Moments of GARCH(p, q)#x2013;Processes.- ARCH(#x221E;) Models and Long Memory Properties.- A Tour in the Asymptotic Theory of GARCH Estimation.- Practical Issues in the Analysis of Univariate GARCH Models.- Semiparametric and Nonparametric ARCH Modeling.- Varying Coefficient GARCH Models.- Extreme Value Theory for GARCH Processes.- Multivariate GARCH Models.- Recent Developments in Stochastic Volatility Modeling.- Stochastic Volatility: Origins and Overview.- Probabilistic Properties of Stochastic Volatility Models.- Moment#x2013;Based Estimation of Stochastic Volatility Models.- Parameter Estimation and Practical Aspects of Modeling Stochastic Volatility.- Stochastic Volatility Models with Long Memory.- Extremes of Stochastic Volatility Models.- Multivariate Stochastic Volatility.- Topics in Continuous Time Processes.- An Overview of Asset–Price Models.- Ornstein–Uhlenbeck Processes and Extensions.- Jump–Type Lévy Processes.- Lévy–Driven Continuous–Time ARMA Processes.- Continuous Time Approximations to GARCH and Stochastic Volatility Models.- Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance.- Parametric Inference for Discretely Sampled Stochastic Differential Equations.- Realized Volatility.- Estimating Volatility in the Presence of Market Microstructure Noise: A Review of the Theory and Practical Considerations.- Option Pricing.- An Overview of Interest Rate Theory.- Extremes of Continuous–Time Processes..- Topics in Cointegration and Unit Roots.- Cointegration: Overview and Development.- Time Series with Roots on or Near the Unit Circle.- Fractional Cointegration.- Special Topics – Risk.- Different Kinds of Risk.- Value–at–Risk Models.- Copula–Based Models for Financial Time Series.- Credit Risk Modeling.- Special Topics – Time Series Methods.- Evaluating Volatility and Correlation Forecasts.- Structural Breaks in Financial Time Series.- An Introduction to Regime Switching Time Series Models.- Model Selection.- Nonparametric Modeling in Financial Time Series.- Modelling Financial High Frequency Data Using Point Processes.- Special Topics – Simulation Based Methods.- Resampling and Subsampling for Financial Time Series.- Markov Chain Monte Carlo.- Particle Filtering.
£284.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Risk and Meaning: Adversaries in Art, Science and
Book SynopsisThis richly illustrated book is an exploration of how chance and risk, on the one hand, and meaning or significance on the other, compete for the limelight in art, in philosophy, and in science. In modern society, prudence and probability calculation permeate our daily lives. Yet it is clear for all to see that neither cautious bank regulations nor mathematics have prevented economic crises from occurring time and again. Nicolas Bouleau argues that it is the meaning we assign to an event that determines the perceived risk, and that we generally turn a blind eye to this important fact, because the word "meaning" is itself awkward to explain. He tackles this fundamental question through examples taken from cultural fields ranging from painting, architecture, and music, to poetry, biology, and astronomy. This enables the reader to view overwhelming risks in a different light. Bouleau clarifies that the most important thing in a time of uncertainty is to think of prudence on a higher level, one that truly addresses the various subjective interpretations of the world.Trade ReviewFrom the reviews:“Risk and Meaning is a quirky book, both in its topic and its physical layout and the writing style that the author adopts … . it is a book that is mathematics-adjacent, and I think that anyone who is able to get past (or even relish) some of the quirkiness in the book will certainly find themselves with plenty to think about. And I’m not sure what more one could ask for in a book.” (Darren Glass, The Mathematical Association of America, November, 2011)Table of ContentsEntrance: Interpretation and Paradigms.- I. Cicero and Divination.- II. Cournot’s "Philosophic Probabilities".- III. Mathematical Probabilities.- IV. Democracy by Chance.- V. Gestalt, Structure, Pattern.- VI. The Third Dimension of Risk.- VII. ''Modern" Architecture.- VIII. The Ideal City.- IX. Daring the Abstract in Art.- X. Saussure or the Dread of Mathematical Probabilities.- XI. Jacques Monod’s Roulette.- XII. From Fortuitism to Animism.- XIII. The Slip as Fortuity and Meaning.- XIV. Guessing Astronomy.- XV. The Legitimacy of Science and Love.- Hints and Index.
£38.24
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers I: Limit Theorems
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume I includes the introductory material, the papers on limit theorems and review articles.Table of ContentsAutobiography: S. R. S. Varadhan.- Introduction: S. R. S. Varadhan.- Prize Citations.- Diffusion Theory by Daniel W. Stroock. - Large Deviations by Daniel W. Stroock.- Large Deviation and Homogenization by Fraydoun Rezakhanlou.- Varadhan's Work on Hydrodynamical Limits by Jeremy Quastel and Horng-Tzer Yau.- Book Review: Multidimensional Diffusion Processes by D. W. Stroock and S. R. S. Varadhan.- Limit Theorems: Limit theorems for sums of independent random variables with values in a Hilbert space.- On the category of indecomposable distributions on topological groups.- Probability distributions on locally compact abelian groups.- Extension of stationary stochastic processes.- Limit theorems in probability.- A limit theorem with strong mixing in Banach space and two applications to stochastic differential equations.- Limit theorems for random walks on Lie groups.- Martingale approach to some limit theorems.- Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions.- Bounding functions of Markov processes and the shortest queue problem.- Finite approximations to quantum systems.- Self-diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion.- Diffusive limit of a tagged particle in asymmetric simple exclusion processes.- A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains.- Review Articles.- Diffusion processes, Stochastic processes: theory and methods.- Stochastic analysis and applications.- Large deviations and entropy, Entropy.- The role of weak convergence in probability theory.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers II: PDE, SDE, Diffusions, Random
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume II includes the papers on PDE, SDE, diffusions, and random media.Table of ContentsVol. II: Diffusion processes with continuous coefficients - I (with D. W. Stroock).- Diffusion processes with continuous coefficients - II (with D. W. Stroock).- Diffusion processes with boundary conditions (with D. W. Stroock).- On degenerate elliptic-parabolic operators of second order and their associated diffusions (with D. W. Stroock).- On the support of diffusion processes with applications to the strong maximum principle (with D. W. Stroock).- Diffusion processes (with D. W. Stroock).- A probabilistic approach to Hp(Rd) (with D. W. Stroock).- Kac functional and Schrodinger equation (with K. L. Chung).- Brownian motion in a wedge with oblique reection (with R. J. Williams).- A multidimensional process involving local time (with A.S. Sznitman).- Etat fondamental et principe du maximum pour les operateurs elliptiques du second ordre dans des domaines generaux. [The ground state and maximum principle for second-order elliptic operators in general domains] (with H. Berestycki and L. Nirenberg).- The principal eigenvalue and maximum principle for second-order elliptic operators in general domains (with H. Berestycki and L. Nirenberg).- Diffusion semigroups and di_usion processes corresponding to degenerate divergence form operators (with J. Quastel).- Random Media.- Diffusion in regions with many small holes (with G. Papanicolaou).- Boundary value problems with rapidly oscillating random coefficients (with G. Papanicolaou).- Diffusions with random coefficients (with G. Papanicolaou).- Ohrnstein-Uhlenbeck process in a random potential (with G. Papanicolaou).- Large deviations for random walks in a random environment.- Random walks in a random environment.- Stochastic homogenization of Hamilton-Jacobi-Bellman equations (with E. Kosygina and F. Rezakhanlou).- Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium (with E. Kosygina).- Behavior of the solution of a random semilinear heat equation (with N. Zygouras).
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers III: Large Deviations
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012.Volume III includes the papers on large deviations. Table of ContentsLarge Deviations.- Asymptotic probabilities and differential equations.- On the behavior of the fundamental solution of the heat equation with variable coefficients .- Diffusion processes in a small time interval .- On a variational formula for the principal eigenvalue for operators with maximum principle.- Asymptotic evaluation of certain Markov process expectations for large time I.- Asymptotic evaluation of certain Markov process expectations for large time II.- Asymptotic evaluation of certain Wiener integrals for large time.- Asymptotics for the Wiener sausage.- Erratum: Asymptotics for the Wiener sausage.- Asymptotic evaluation of certain Markov process expectations for large time III.- On the principal eigenvalue of second-order elliptic differential operators.- On laws of the iterated logarithm for local times.- Some problems of large deviations.- On the number of distinct sites visited by a random walk.- A law of the iterated logarithm for total occupation times of transient Brownian motion.- Some problems of large deviations .- The polaron problem and large deviations.- Asymptotic evaluation of certain Markov process expectations for large time IV.- Asymptotics for the polaron.- Large deviations for stationary Gaussian processes.- Large deviations and applications.- Large deviations for non-interacting infinite-particle systems.- Some familiar examples for which the large deviation principle does not hold.- The large deviation principle for the Erdös-Rényi random graph.- Large deviations for random matrices.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Collected Papers IV: Particle Systems and Their
Book SynopsisFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputation as one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume IV includes the papers on particle systems.Table of ContentsVolume 4: Particle Systems and Their Large Deviations.- Nonlinear diffusion limit for a system with nearest neighbor interaction.- Hydrodynamics and large deviation for simple exclusion processes.- Large deviations from a hydrodynamic scaling limit.- On the derivation of conservation laws for stochastic dynamics.- Scaling limits for interacting diffusions.- Scaling limit for interacting Ornstein-Uhlenbeck processes.- Entropy methods in hydrodynamical scaling.- Hydrodynamical limit for a Hamiltonian system with weak noise.- Nonlinear diffusion limit for a system with nearest neighbor interactions II.- Regularity of self-diffusion coefficient.- Entropy methods in hydrodynamic scaling.- Spectral gap for zero-range dynamics.- The complex story of simple exclusion.- Non-gradient models in hydrodynamic scaling.- Relative entropy and mixing properties of interacting particle systems.- Diffusive limit of lattice gas with mixing conditions.- Large deviations for the symmetric simple exclusion process in dimensions d > 3.- Large deviations for interacting particle systems.- Infinite particle systems and their scaling limits.- Lectures on hydrodynamic scaling.- Scaling limits of large interacting systems .- Asymptotic behavior of a tagged particle in simple exclusion processes.- Large deviation and hydrodynamic scaling.- Symmetric simple exclusion process: regularity of the self-diffusion coefficient.- Finite-dimensional approximation of the self-diffusion coefficient for the exclusion process.- Large deviations for the asymmetric simple exclusion process.- Diffusive behaviour of the equilibrium fluctuations in the asymmetric exclusion processes.- On viscosity and fluctuation-dissipation in exclusion processes.- Large deviations for the current and tagged particle in 1d nearest neighbor.- Symmetric simple exclusion.- List of Publications of S.R.S. Varadhan.- Acknowledgements.
£80.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Long-Memory Processes: Probabilistic Properties
Book SynopsisLong-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.Trade ReviewFrom the book reviews:“This encyclopaedic book covers almost the whole literature on univariate and multivariate long-range dependent (LRD) processes, or long-memory processes or strongly dependent processes. … This volume is then of strong interest for both researchers and teachers familiar with the topic, as it gives an overall, structured and balanced picture of the current state of the art. Readers less familiar with the topic will easily find their way in the vast literature on this issue, and will have their curiosity satisfied.” (Gilles Teyssière, Mathematical Reviews, October, 2014)“This book aims to cover probabilistic and statistical aspects of long-memory processes in as much detail as possible, including a broad range of topics. The authors did an excellent job to reach their goals, and the book would be a must for researchers interested in long-memory processes and practioners on time series and data analysis. … the book is an excellent choice for anyone who is working in fields related to long-memory processes with many update information and research topics.” (Weiping Li, zbMATH, Vol. 1282, 2014)Table of ContentsDefinition of Long Memory.- Origins and Generation of Long Memory.- Mathematical Concepts.- Limit Theorems.- Statistical Inference for Stationary Processes.- Statistical Inference for Nonlinear Processes.- Statistical Inference for Nonstationary Processes.- Forecasting.- Spatial and Space-Time Processes.- Resampling.- Function Spaces.- Regularly Varying Functions.- Vague Convergence.- Some Useful Integrals.- Notation and Abbreviations.
£151.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Analyzing Compositional Data with R
Book SynopsisThis book presents the statistical analysis of compositional data sets, i.e., data in percentages, proportions, concentrations, etc. The subject is covered from its grounding principles to the practical use in descriptive exploratory analysis, robust linear models and advanced multivariate statistical methods, including zeros and missing values, and paying special attention to data visualization and model display issues. Many illustrated examples and code chunks guide the reader into their modeling and interpretation. And, though the book primarily serves as a reference guide for the R package “compositions,” it is also a general introductory text on Compositional Data Analysis. Awareness of their special characteristics spread in the Geosciences in the early sixties, but a strategy for properly dealing with them was not available until the works of Aitchison in the eighties. Since then, research has expanded our understanding of their theoretical principles and the potentials and limitations of their interpretation. This is the first comprehensive textbook addressing these issues, as well as their practical implications with regard to software.The book is intended for scientists interested in statistically analyzing their compositional data. The subject enjoys relatively broad awareness in the geosciences and environmental sciences, but the spectrum of recent applications also covers areas like medicine, official statistics, and economics. Readers should be familiar with basic univariate and multivariate statistics. Knowledge of R is recommended but not required, as the book is self-contained.Trade ReviewFrom the reviews:“This book offers not only the theoretical background to analyse and interpret compositional data, but also the R support and guidance for the compositions package. The book is organised in 7 chapters. … The book is built in an accessible manner for undergraduates and postgraduates alike and offers an all in one overview of the analysis of compositional data in R.” (Irina Ioana Mohorianu, zbMATH, Vol. 1276, 2014)Table of ContentsIntroduction.- Fundamental Concepts of Compositional Data Analysis.- Distributions for Random Compositions.- Descriptive Analysis of Compositional Data.- Linear Models for Compositions.- Multivariate Statistics.- Zeroes, Missings and Outliers.- References.- Index.
£39.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG One-Dimensional Dynamics
Book SynopsisOne-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).Table of Contents0. Introduction.- I. Circle Diffeomorphisms.- 1. The Combinatorial Theory of Poincaré.- 2. The Topological Theory of Denjoy.- 2.a The Denjoy Inequality.- 2.b Ergodicity.- 3. Smooth Conjugacy Results.- 4. Families of Circle Diffeomorphisms; Arnol’d tongues.- 5. Counter-Examples to Smooth Linearizability.- 6. Frequency of Smooth Linearizability in Families.- 7. Some Historical Comments and Further Remarks.- II. The Combinatorics of One-Dimensional Endomorphisms.- 1. The Theorem of Sarkovskii.- 2. Covering Maps of the Circle as Dynamical Systems.- 3. The Kneading Theory and Combinatorial Equivalence.- 3.a Examples.- 3.b Hofbauer’s Tower Construction.- 4. Full Families and Realization of Maps.- 5. Families of Maps and Renormalization.- 6. Piecewise Monotone Maps can be Modelled by Polynomial Maps.- 7. The Topological Entropy.- 8. The Piecewise Linear Model.- 9. Continuity of the Topological Entropy.- 10. Monotonicity of the Kneading Invariant for the Quadratic Family.- 11. Some Historical Comments and Further Remarks.- III. Structural Stability and Hyperbolicity.- 1. The Dynamics of Rational Mappings.- 2. Structural Stability and Hyperbolicity.- 3. Hyperbolicity in Maps with Negative Schwarzian Derivative.- 4. The Structure of the Non-Wandering Set.- 5. Hyperbolicity in Smooth Maps.- 6. Misiurewicz Maps are Almost Hyperbolic.- 7. Some Further Remarks and Open Questions.- IV. The Structure of Smooth Maps.- 1. The Cross-Ratio: the Minimum and Koebe Principle.- l.a Some Facts about the Schwarzian Derivative.- 2. Distortion of Cross-Ratios.- 2.a The Zygmund Conditions.- 3. Koebe Principles on Iterates.- 4. Some Simplifications and the Induction Assumption.- 5. The Pullback of Space: the Koebe/Contraction Principle.- 6. Disjointness of Orbits of Intervals.- 7. Wandering Intervals Accumulate on Turning Points.- 8. Topological Properties of a Unimodal Pullback.- 9. The Non-Existence of Wandering Intervals.- 10. Finiteness of Attractors.- 11. Some Further Remarks and Open Questions.- V. Ergodic Properties and Invariant Measures.- 1. Ergodicity, Attractors and Bowen-Ruelle-Sinai Measures.- 2. Invariant Measures for Markov Maps.- 3. Constructing Invariant Measures by Inducing.- 4. Constructing Invariant Measures by Pulling Back.- 5. Transitive Maps Without Finite Continuous Measures.- 6. Frequency of Maps with Positive Liapounov Exponents in Families and Jakobson’s Theorem.- 7. Some Further Remarks and Open Questions.- VI. Renormalization.- 1. The Renormalization Operator.- 2. The Real Bounds.- 3. Bounded Geometry.- 4. The PullBack Argument.- 5. The Complex Bounds.- 6. Riemann Surface Laminations.- 7. The Almost Geodesic Principle.- 8. Renormalization is Contracting.- 9. Universality of the Attracting Cantor Set.- 10. Some Further Remarks and Open Questions.- VII. Appendix.- 1. Some Terminology in Dynamical Systems.- 2. Some Background in Topology.- 3. Some Results from Analysis and Measure Theory.- 4. Some Results from Ergodic Theory.- 5. Some Background in Complex Analysis.- 6. Some Results from Functional Analysis.
£104.49
