Probability and statistics Books

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Book SynopsisDrawing on his Elements of Physical Biology (1925) and most of his mathematical papers, Latka offered French readers insights into his biological thought and a concise and mathematically accessible summary of what he called recent contributions in demographic analy­ sis.Table of ContentsPrinciples: 1. On Evolution in Organic and Inorganic Systems. 2. On the Direction of Time. 3. On Energetics and Uncertainty. 4. Biological Stoichiometry. Demographic Analysis with Specific Application to the Human Species: 1. Introduction. 2. Relations Involving Mortality and Births. 3. Relations Involving Fertility. 4. The Progeny of a Population Element. 5. Indices and Measures of Natural Increase. 6. Relations Involving Fertility by Birth Order. 7. Relations Involving the Survival Functions of Two Individuals. 8. Extinction of a Line of Descent. 9. Conclusion. Appendix. Bibliography. Author Index. Subject Index.

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Book SynopsisPricing by Arbitrage.- Martingale Measures.- The First Fundamental Theorem.- Complete Markets.- Discrete-time American Options.- Continuous-Time Stochastic Calculus.- Continuous-Time European Options.- The American Put Option.- Bonds and Term Structure.- Consumption-Investment Strategies.- Measures of Risk.Trade ReviewFrom the reviews: "...This book is a valuable addition to a graduate student's reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." SIAM Review, December 2005 From the reviews of the second edition: "The book is very carefully formatted. … this book is a valuable addition to a graduate student’s reference collection. The number of textbooks in mathematical finance is increasing much faster than the number of revolutionary contributions to the field, but this text stands above the crowd." (Alexandre D’Aspremont, SIAM Reviews, December, 2005) "The emphasis of the first edition of this book was on developing the mathematical concepts for the rapidly expanding field of mathematical finance. This second edition contains a significant number of changes and additions … . The target audience is readers with sound mathematical background on elementary concepts from measure-theoretic probability … . It should be an equally valuable resource to practitioners interested in the mathematical tools … . will be a very useful addition to any scholarly library." (Theofanis Sapatinas, Journal of Applied Sciences, Vol. 32 (6), 2005) "The second edition adds new matieral from current active research areas. A new chapter on coherent risk measures for instance reflects the recent trend in research and applications in the area of risk management. In summary, this is an excellent textbook in mathematical finance, and I can definitely recommend it." (S. Peng, Short Book Reviews of the ISI, June 2006)Table of ContentsPricing by Arbitrage * Martingale Measures * The Fundamental Theorem of Asset Pricing * Complete Markets and Martingale Representation * Stopping Times and American Options * A Review of Continuous Time Stochastic Calculus * European Options in Continuous Time * The American Option * Bonds and Term Structure * Consumption-Investment Strategies *

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Book SynopsisThis book summarizes current knowledge regarding the theory of estimation for semiparametric models with missing data, in an organized and comprehensive manner.Trade ReviewFrom the reviews: "The author, who does not need an introduction…had presented with clarity how he views three different subjects within a unified approach for statistical inference.…It is a long awaited book for a large audience of graduate students and researchers who have often found this subject matter daunting.… It is an easy decision for me to recommend this book to anyone who is interested in learning and using theories of frequentist estimation for semiparametric models and coarsened data. Even beyond his/her graduate student days, any statistical researcher interested in mastering frequentist semiparamatric estimation can pick up all the essential information from this book." (Debajyoti Sinha, American Statistical Association, JASA, March 2009, Vol. 104, No. 485) "Since much of the work in this area is very technical, it is most welcome to have a self-contained clearly written account by a highly-regarded author. The application to missing data is also clearly of great interest." R.J.A. Little for Short Book Reviews of the ISI, December 2006 "This book is focused precisely on the problem of estimation for a semiparametric model when the data are missing. This comprehensive monograph offers an in-depth look at the associated theory … . It was a great pleasure to read this masterful account of semiparametric theory for missing data problems … . It provides a valuable resource because it contains an up-to-date literature review and an exceptional account of state of the art research on the necessary theory. … I recommend it to any professional statistician." (Konstantinos Fokianos, Technometrics, Vol. 49 (2), 2007) "The book under review deals with estimation for SMs with missing, coarsened, and censored data. … The book is very clearly and informally written. The exposition is instructive and rigorous enough. There are many important examples, oriented to biomedical applications. The monograph will be useful for graduate and post-graduate students in statistics and biostatistics, as well as researchers in statistics and survival analysis." (Oleksandr Kukush, Zentralblatt MATH, Vol. 1105 (7), 2007)Table of Contentsto Semiparametric Models.- Hilbert Space for Random Vectors.- The Geometry of Influence Functions.- Semiparametric Models.- Other Examples of Semiparametric Models.- Models and Methods for Missing Data.- Missing and Coarsening at Random for Semiparametric Models.- The Nuisance Tangent Space and Its Orthogonal Complement.- Augmented Inverse Probability Weighted Complete-Case Estimators.- Improving Efficiency and Double Robustness with Coarsened Data.- Locally Efficient Estimators for Coarsened-Data Semiparametric Models.- Approximate Methods for Gaining Efficiency.- Double-Robust Estimator of the Average Causal Treatment Effect.- Multiple Imputation: A Frequentist Perspective.

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Book SynopsisStatistical Preliminaries.- Bayesian Inference and Decision Theory.- Utility, Prior, and Bayesian Robustness.- Large Sample Methods.- Choice of Priors for Low-dimensional Parameters.- Hypothesis Testing and Model Selection.- Bayesian Computations.- Some Common Problems in Inference.- High-dimensional Problems.- Some Applications.Trade ReviewFrom the reviews: "This text provides a unique blend of theory, methods and applications that is suitable for a one-semester course in Bayesian analysis." C.M. O'Brien for Short Book Reviews of the ISI, December 2006 "The material of the book covers more than a one semester course and provides enough results for a second course. … the book is simultaneously useful for different readership groups. Instructors will get guidelines for preparing a course on Bayesian statistics … . Students will enjoy the excellently clear … style and the exercises at the end of each chapter. Practitioners will find plenty of classical and recent Bayesian methods. … I highly recommend the book to all readers who are interested in Bayesian statistics." (Friedrich Liese, Mathematical Reviews, Issue, 2007 g) "This book, with its 10 chapters, represents a valuable introduction to Bayesian statistics and varies among theory, methods and applications. … The book’s material is invaluable, and is presented with clarity … . Each chapter’s topics are covered by various examples and many exercises. … gives a constructive approach to the statistical analysis based on Bayes’ formula. … So, it is strongly recommended to libraries and all who are interested in statistics." (Hassan S. Bakouch, Journal of Applied Statistics, Vol. 35 (3), 2008) "Taken overall, the book should be recommended to a wide audience...as a source of interesting and mind-provoking information about Bayesian statistics. " ( ISCB News, 2008) "Bayesian analysis have arrived. … This text offers one approach based on the pedagogic decision to ‘balance theory, methods, and applications.’ … The brief introduction to classical inference … provides a nice basis for the objective Bayesian treatment offered by the authors throughout the book. … this book appealing for classically trained statisticians. … Overall, I congratulate the authors for a largely successful attempt to introduce true religion." (C. Shane Reese, Journal of the American Statistical Association, Vol. 103 (482), June, 2008) "The book under review aims to contribute to existing graduate-level introductory texts on Bayesian analysis by providing an impressive blend of theory, methods, and applications. It consists of 10 chapters and 5 appendices." (Joseph Melamed, Zentralblatt MATH, Vol. 1135 (13), 2008) "This book is an introduction to the theory and methods underlying Bayesian statistics written by three absolute experts on the field. It is primarily intended for graduate students taking a first course in Bayesian analysis or instructors preparing an introductory one-semester course on Bayesian analysis. … The book is written in a clear, relatively mathematical style … ." (Björn Bornkamp, Advances in Statistical Analysis, Issue 1, 2009) "This book introduces the mathematical theory of Bayesian analysis along the statistical line of decision theory. … This book is intended as a graduate-level analysis of mathematical problems in Bayesian statistics and can in parts be used as textbook on Bayesian theory. … Overall, if I had to recommend a good book on new advancements of Bayesian statistics in the last decade from a theoretical decision point of view, I would recommend this book." (Wolfgang Polasek, Statistical Papers, Vol. 50, 2009)Table of ContentsStatistical Preliminaries.- Bayesian Inference and Decision Theory.- Utility, Prior, and Bayesian Robustness.- Large Sample Methods.- Choice of Priors for Low-dimensional Parameters.- Hypothesis Testing and Model Selection.- Bayesian Computations.- Some Common Problems in Inference.- High-dimensional Problems.- Some Applications.

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Book SynopsisThis greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics.Trade ReviewFrom the reviews of the second edition:“The second edition of the praised classic without whom I know that some people never leave home … . attempts to bring these uses to the fore so that the reader can see the extent and variation in its use. The chapters of the original version remain intact … . The bibliography has increased by over 50%. … Needless to say, the revised volume obviously continues as a celebrated classic.” (Simo Puntanen, International Statistical Review, Vol. 79 (2), 2011)Table of ContentsIntroduction.- Doubly Stochastic Matrices.- Schur-Convex Functions.- Equivalent Conditions for Majorization.- Preservation and Generation of Majorization.- Rearrangements and Majorization.- Combinatorial Analysis.- Geometric Inequalities.- Matrix Theory.- Numerical Analysis.- Stochastic Majorizations.- Probabilistic, Statistical, and Other Applications.- Additional Statistical Applications.- Orderings Extending Majorization.- Multivariate Majorization.- Convex Functions and Some Classical Inequalities.- Stochastic Ordering.- Total Positivity.- Matrix Factorizations, Compounds, Direct Products, and M-Matrices.- Extremal Representations of Matrix Functions.

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Book SynopsisNow available in paperback, this book provides a comprehensive account of survey sampling theory and methodology suitable for students and researchers across a variety of disciplines. The first textbook that systematically extends traditional sampling theory with the aid of a modern model assisted outlook.Trade Review"I would recommend that this book be in the office of every survey methodologist."(Journal of Official Statistics)Table of ContentsI Principles of Estimation for Finite Populations and Important Sampling Designs.- 1 Survey Sampling in Theory and Practice.- 1.1 Surveys in Society.- 1.2 Skeleton Outline of a Survey.- 1.3 Probability Sampling.- 1.4 Sampling Frame.- 1.5 Area Frames and Similar Devices.- 1.6 Target Population and Frame Population.- 1.7 Survey Operations and Associated Sources of Error.- 1.8 Planning a Survey and the Need for Total Survey Design.- 1.9 Total Survey Design.- 1.10 The Role of Statistical Theory in Survey Sampling.- Exercises.- 2 Basic Ideas in Estimation from Probability Samples.- 2.1 Introduction.- 2.2 Population, Sample, and Sample Selection.- 2.3 Sampling Design.- 2.4 Inclusion Probabilities.- 2.5 The Notion of a Statistic.- 2.6 The Sample Membership Indicators.- 2.7 Estimators and Their Basic Statistical Properties.- 2.8 The ? Estimator and Its Properties.- 2.9 With-Replacement Sampling.- 2.10 The Design Effect.- 2.11 Confidence Intervals.- Exercises.- 3 Unbiased Estimation for Element Sampling Designs.- 3.1 Introduction.- 3.2 Bernoulli Sampling.- 3.3 Simple Random Sampling.- 3.3.1 Simple Random Sampling without Replacement.- 3.3.2 Simple Random Sampling with Replacement.- 3.4 Systematic Sampling.- 3.4.1 Definitions and Main Result.- 3.4.2 Controlling the Sample Size.- 3.4.3 The Efficiency of Systematic Sampling.- 3.4.4 Estimating the Variance.- 3.5 Poisson Sampling.- 3.6 Probability Proportional-to-Size Sampling.- 3.6.1 Introduction.- 3.6.2 ?ps Sampling.- 3.6.3 pps Sampling.- 3.6.4 Selection from Randomly Formed Groups.- 3.7 Stratified Sampling.- 3.7.1 Introduction.- 3.7.2 Notation, Definitions, and Estimation.- 3.7.3 Optimum Sample Allocation.- 3.7.4 Alternative Allocations under STSI Sampling.- 3.8 Sampling without Replacement versus Sampling with Replacement.- 3.8.1 Alternative Estimators for Simple Random Sampling with Replacement.- 3.8.2 The Design Effect of Simple Random Sampling with Replacement.- Exercises.- 4 Unbiased Estimation for Cluster Sampling and Sampling in Two or More Stages.- 4.1 Introduction.- 4.2 Single-Stage Cluster Sampling.- 4.2.1 Introduction.- 4.2.2 Simple Random Cluster Sampling.- 4.3 Two-Stage Sampling.- 4.3.1 Introduction.- 4.3.2 Two-Stage Element Sampling.- 4.4 Multistage Sampling.- 4.4.1 Introduction and a General Result.- 4.4.2 Three-Stage Element Sampling.- 4.5 With-Replacement Sampling of PSUs.- 4.6 Comparing Simplified Variance Estimators in Multistage Sampling.- Exercises.- 5 Introduction to More Complex Estimation Problems.- 5.1 Introduction.- 5.2 The Effect of Bias on Confidence Statements.- 5.3 Consistency and Asymptotic Unbiasedness.- 5.4 ? Estimators for Several Variables of Study.- 5.5 The Taylor Linearization Technique for Variance Estimation.- 5.6 Estimation of a Ratio.- 5.7 Estimation of a Population Mean.- 5.8 Estimation of a Domain Mean.- 5.9 Estimation of Variances and Covariances in a Finite Population.- 5.10 Estimation of Regression Coefficients.- 5.10.1 The Parameters of Interest.- 5.10.2 Estimation of the Regression Coefficients.- 5.11 Estimation of a Population Median.- 5.12 Demonstration of Result 5.10.1.- Exercises.- II Estimation through Linear Modeling, Using Auxiliary Variables.- 6 The Regression Estimator.- 6.1 Introduction.- 6.2 Auxiliary Variables.- 6.3 The Difference Estimator.- 6.4 Introducing the Regression Estimator.- 6.5 Alternative Expressions for the Regression Estimator.- 6.6 The Variance of the Regression Estimator.- 6.7 Comments on the Role of the Model.- 6.8 Optimal Coefficients for the Difference Estimator.- Exercises.- 7 Regression Estimators for Element Sampling Designs.- 7.1 Introduction.- 7.2 Preliminary Considerations.- 7.3 The Common Ratio Model and the Ratio Estimator.- 7.3.1 The Ratio Estimator under SI Sampling.- 7.3.2 The Ratio Estimator under Other Designs.- 7.3.3 Optimal Sampling Design for the ? Weighted Ratio Estimator.- 7.3.4 Alternative Ratio Models.- 7.4 The Common Mean Model.- 7.5 Models Involving Population Groups.- 7.6 The Group Mean Model and the Poststratified Estimator.- 7.7 The Group Ratio Model and the Separate Ratio Estimator.- 7.8 Simple Regression Models and Simple Regression Estimators.- 7.9 Estimators Based on Multiple Regression Models.- 7.9.1 Multiple Regression Models.- 7.9.2 Analysis of Variance Models.- 7.10 Conditional Confidence Intervals.- 7.10.1 Conditional Analysis for BE Sampling.- 7.10.2 Conditional Analysis for the Poststratification Estimator.- 7.11 Regression Estimators for Variable-Size Sampling Designs.- 7.12 A Class of Regression Estimators.- 7.13 Regression Estimation of a Ratio of Population Totals.- Exercises.- 8 Regression Estimators for Cluster Sampling and Two-Stage Sampling.- 8.1 Introduction.- 8.2 The Nature of the Auxiliary Information When Clusters of Elements Are Selected.- 8.3 Comments on Variance and Variance Estimation in Two-Stage Sampling.- 8.4 Regression Estimators Arising Out of Modeling at the Cluster Level.- 8.5 The Common Ratio Model for Cluster Totals.- 8.6 Estimation of the Population Mean When Clusters Are Sampled.- 8.7 Design Effects for Single-Stage Cluster Sampling.- 8.8 Stratified Clusters and Poststratified Clusters.- 8.9 Regression Estimators Arising Out of Modeling at the Element Level.- 8.10 Ratio Models for Elements.- 8.11 The Group Ratio Model for Elements.- 8.12 The Ratio Model Applied within a Single PSU.- Exercises.- III Further Questions in Design and Analysis of Surveys.- 9 Two-Phase Sampling.- 9.1 Introduction.- 9.2 Notation and Choice of Estimator.- 9.3 The ?* Estimator.- 9.4 Two-Phase Sampling for Stratification.- 9.5 Auxiliary Variables for Selection in Two Phases.- 9.6 Difference Estimators.- 9.7 Regression Estimators for Two-Phase Sampling.- 9.8 Stratified Bernoulli Sampling in Phase Two.- 9.9 Sampling on Two Occasions.- 9.9.1 Estimating the Current Total.- 9.9.2 Estimating the Previous Total.- 9.9.3 Estimating the Absolute Change and the Sum of the Totals.- Exercises.- 10 Estimation for Domains.- 10.1 Introduction.- 10.2 The Background for Domain Estimation.- 10.3 The Basic Estimation Methods for Domains.- 10.4 Conditioning on the Domain Sample Size.- 10.5 Regression Estimators for Domains.- 10.6 A Ratio Model for Each Domain.- 10.7 Group Models for Domains.- 10.8 Problems Arising for Small Domains; Synthetic Estimation.- 10.9 More on the Comparison of Two Domains.- Exercises.- 11 Variance Estimation.- 11.1 Introduction.- 11.2 A Simplified Variance Estimator under Sampling without Replacement.- 11.3 The Random Groups Technique.- 11.3.1 Independent Random Groups.- 11.3.2 Dependent Random Groups.- 11.4 Balanced Half-Samples.- 11.5 The Jackknife Technique.- 11.6 The Bootstrap.- 11.7 Concluding Remarks.- Exercises.- 12 Searching for Optimal Sampling Designs.- 12.1 Introduction.- 12.2 Model-Based Optimal Design for the General Regression Estimator.- 12.3 Model-Based Optimal Design for the Group Mean Model.- 12.4 Model-Based Stratified Sampling.- 12.5 Applications of Model-Based Stratification.- 12.6 Other Approaches to Efficient Stratification.- 12.7 Allocation Problems in Stratified Random Sampling.- 12.8 Allocation Problems in Two-Stage Sampling.- 12.8.1 The ? Estimator of the Population Total.- 12.8.2 Estimation of the Population Mean.- 12.9 Allocation in Two-Phase Sampling for Stratification.- 12.10 A Further Comment on Mathematical Programming.- 12.11 Sampling Design and Experimental Design.- Exercises.- 13 Further Statistical Techniques for Survey Data.- 13.1 Introduction.- 13.2 Finite Population Parameters in Multivariate Regression and Correlation Analysis.- 13.3 The Effect of Sampling Design on a Statistical Analysis.- 13.4 Variances and Estimated Variances for Complex Analyses.- 13.5 Analysis of Categorical Data for Finite Populations.- 13.5.1 Test of Homogeneity for Two Populations.- 13.5.2 Testing Homogeneity for More than Two Finite Populations.- 13.5.3 Discussion of Categorical Data Tests for Finite Populations.- 13.6 Types of Inference When a Finite Population Is Sampled.- Exercises.- IV A Broader View of Errors in Surveys.- 14 Nonsampling Errors and Extensions of Probability Sampling Theory.- 14.1 Introduction.- 14.2 Historic Notes: The Evolution ofthe Probability Sampling Approach.- 14.3 Measurable Sampling Designs.- 14.4 Some Nonprobability Sampling Methods.- 14.5 Model-Based Inference from Survey Samples.- 14.6 Imperfections in the Survey Operations.- 14.6.1 Ideal Conditions for the Probability Sampling Approach.- 14.6.2 Extension of the Probability Sampling Approach.- 14.7 Sampling Frames.- 14.7.1 Frame Imperfections.- 14.7.2 Estimation in the Presence of Frame Imperfections.- 14.7.3 Multiple Frames.- 14.7.4 Frame Construction and Maintenance.- 14.8 Measurement and Data Collection.- 14.9 Data Processing.- 14.10 Nonresponse.- Exercises.- 15 Nonresponse.- 15.1 Introduction.- 15.2 Characteristics of Nonresponse.- 15.2.1 Definition of Nonresponse.- 15.2.2 Response Sets.- 15.2.3 Lack of Unbiased Estimators.- 15.3 Measuring Nonresponse.- 15.4 Dealing with Nonresponse.- 15.4.1 Planning of the Survey.- 15.4.2 Callbacks and Follow-Ups.- 15.4.3 Subsampling of Nonrespondents.- 15.4.4 Randomized Response.- 15.5 Perspectives on Nonresponse.- 15.6 Estimation in the Presence of Unit Nonresponse.- 15.6.1 Response Modeling.- 15.6.2 A Useful Response Model.- 15.6.3 Estimators That Use Weighting Only.- 15.6.4 Estimators That Use Weighting as Well as Auxiliary Variables.- 15.7 Imputation.- Exercises.- 16 Measurement Errors.- 16.1 Introduction.- 16.2 On the Nature of Measurement Errors.- 16.3 The Simple Measurement Model.- 16.4 Decomposition of the Mean Square Error.- 16.5 The Risk of Underestimating the Total Variance.- 16.6 Repeated Measurements as a Tool in Variance Estimation.- 16.7 Measurement Models Taking Interviewer Effects into Account.- 16.8 Deterministic Assignment of Interviewers.- 16.9 Random Assignment of Interviewers to Groups.- 16.10 Interpenetrating Subsamples.- 16.11 A Measurement Model with Sample-Dependent Moments.- Exercises.- 17 Quality Declarations for Survey Data.- 17.1 Introduction.- 17.2 Policies Concerning Information on Data Quality.- 17.3 Statistics Canada’s Policy on Informing Users of Data Quality and Methodology.- Exercise.- Appendix A Principles of Notation.- Appendix B The MU284 Population.- Appendix C The Clustered MU284 Population.- Appendix D The CO124 Population.- References.- Answers to Selected Exercises.- Author Index.

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Book SynopsisData management and software.- Advice for teachers.- Exploration.- Linear regression.- Generalised linear modelling.- Additive and generalised additive modelling.- to mixed modelling.- Univariate tree models.- Measures of association.- Ordination First encounter.- Principal component analysis and redundancy analysis.- Correspondence analysis and canonical correspondence analysis.- to discriminant analysis.- Principal coordinate analysis and non-metric multidimensional scaling.- Time series analysis Introduction.- Common trends and sudden changes.- Analysis and modelling of lattice data.- Spatially continuous data analysis and modelling.- Univariate methods to analyse abundance of decapod larvae.- Analysing presence and absence data for flatfish distribution in the Tagus estuary, Portugal.- Crop pollination by honeybees in Argentina using additive mixed modelling.- Investigating the effects of rice farming on aquatic birds with mixed modelling.- Classification trees and radar detectioTrade ReviewFrom the reviews: "I liked the compact style of the book and really enjoyed the case studies. The book would be a suitable companion to statistics courses for both ecologists and statisticians at the introductory graduate level….All in all, I enjoyed reading the book and marvel at the wide range of sophisticated statistical models used in modern ecology."(Biometrics, 64, March 2008) "Readership: Undergraduates, postgraduates and scientists engaged in areas of the environmental sciences and ecological research. The material presented in this book has been developed and used by the authors in teaching statistics to its intended readership. The text is divided into two parts … . I have no doubt that for undergraduate students the main strength of the book will be the breadth of topics covered by the case studies – ranging from terrestrial ecology to marine biology." (C. M. O’Brien, International Statistical Review, Vol. 75 (3), 2007) "This is a practical way of analysing ecological data in which methodological approaches are combined with real data sets with the advantages and disadvantages of each strategy discussed. Who is it for? Upper undergraduates, postgraduates and researchers in ecology. Presentation It links ecological data, data analysis and discussion of the approaches. Would you recommend it? If you want an edited volume on different methods of ecological data analysis, then this book is worth looking through." (Times Higher Education, May, 2008) "The book is aimed at three types of readers: ecologists who wish to develop their own statistical skills, quantitative ecologists who want to use more advanced techniques, and statistical scientists seeking more experience analyzing ecological data. … Enjoyable aspects of the book include good graphical outputs, with interpretations, in the text. … Overall, this book is wroth the purchase price … . No other book combines as many good ecological data sets with such thoughtfully written analyses. I give this book two enthusiastic thumbs up!" (Loveday Conquest, Journal of the American Statistical Asociation, Vol. 103 (483), September, 2008) "The book aims to give readers sufficient information to apply statistical methodology in a correct and useful way. … the book meets its aim, covering a wide range of statistical techniques and dealing with many situations that are encountered in ecological statistics. This is an excellent, nicely presented and very readable book. I would highly recommend it to numerate researchers and students interested in environment and ecological data analysis." (Weiqi Luo, Journal of Applied Statistics, Vol. 36 (2), February, 2009) "Analysing Ecological Data by a group of ecologists-gone-statisticians from Scotland is the latest book in this area and based on years of teaching and consultancy experience. … The book differs from many of its competitors in its structure: it contains a general introduction to several fields of descriptive ecological data analysis (370 pages), which is augmented with 17 chapter-length case studies … . In summary, I can recommend the book primarily as advanced material for ecologists … ." (Carsten F. Dormann, Basic and Applied Ecology, Vol. (10), 2009)Table of ContentsIntroduction.- Data management and software.- Advice for teachers.- Exploration.- Linear regression.- Generalised linear modelling.- Additive and generalised additive modelling.- Introduction to mixed modelling.- Univariate tree models.- Measures of association.- Ordination--first encounter.- Principal component analysis and redundancy analysis.- Correspondence analysis and canonical correspondence analysis.- Introduction to discriminant analysis.- Principal coordinate analysis and non-metric multidimensional scaling.- Time series analysis--Introduction.- Common trends and sudden changes.- Analysis and modelling lattice data.- Spatially continuous data analysis and modelling.- Univariate methods to analyse abundance of decapod larvae.- Analysing presence and absence data for flatfish distribution in the Tagus estuary, Portugual.- Crop pollination by honeybees in an Argentinean pampas system using additive mixed modelling.- Investigating the effects of rice farming on aquatic birds with mixed modelling.- Classification trees and radar detection of birds for North Sea wind farms.- Fish stock identification through neural network analysis of parasite fauna.- Monitoring for change: using generalised least squares, nonmetric multidimensional scaling, and the Mantel test on western Montana grasslands.- Univariate and multivariate analysis applied on a Dutch sandy beach community.- Multivariate analyses of South-American zoobenthic species--spoilt for choice.- Principal component analysis applied to harbour porpoise fatty acid data.- Multivariate analysis of morphometric turtle data--size and shape.- Redundancy analysis and additive modelling applied on savanna tree data.- Canonical correspondence analysis of lowland pasture vegetation in the humid tropics of Mexico.- Estimating common trends in Portuguese fisheries landings.- Common trends in demersal communities on the Newfoundland-Labrador Shelf.- Sea level change and salt marshes in the Wadden Sea: a time series analysis.- Time series analysis of Hawaiian waterbirds.- Spatial modelling of forest community features in the Volzhsko-Kamsky reserve.

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Book SynopsisStructured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.Trade ReviewFrom the reviews:MATHEMATICAL REVIEWS"This is indeed an invaluable text for students in information technology, engineering, and statistics. It is also very helpful for researchers in these fields and for those working in industry. The book is self-contained…The book has enough illustrative examples and exercises for the reader. All the illustrations are motivated by real applications. Moreover, the book provides a good balance between pure mathematical treatment and the applied aspects of the subject.""The Bayesian network (BN), or probabilistic expert system, is technology for automating human-life reasoning under uncertainty in specific contexts. … the book does an admirable job of concisely explaining a great range of concepts and techniques. … the book is very well written and to my knowledge nothing else meets its specific goal of quickly equipping the reader with both practical skills and sufficient theoretical background. … I certainly would not want to try to implement a BN application without reading this book.” (David Tritchler, Sankhya: Indian Journal of Statistics, Vol. 64 (B Part 3), 2002)"Professor Jensen is certainly one of the most influential researchers in the field of Bayesian networks and it is not surprising that this book represents a very clear and useful presentation of the main properties and use of graphical models. … I think that the present volume represents a useful integration of other material and a compact guide for either a student who wants an introduction to the field or a teacher who needs a reference for a course on probabilistic reasoning in AI." (Luigi Portinale, The Computer Journal, Vol. 46 (3), 2003)"This book is an introduction to Bayesian networks at an accessible level for first-year graduate or advanced undergraduate students. … I found this book to be an excellent introduction to the topic. It is well written, provides broad topic coverage, and is quite accessible to the non-expert. … I think Bayesian Networks and Decision Graphs would make a fine text for an introductory class in Bayesian networks or a useful reference for anyone interested in learning about the field." (David J. Marchette, Technometrics, Vol. 45 (2), 2003)"I can comfortably recommend this book as a primary source for topics related to Bayesian networks and decision graphs. This would be an excellent edition to any personal library." (Technometrics, Feburary 2008)From the reviews of the second edition:"The present book provides a very readable but also rigorous and comprehensive introduction to the subject. It would make a very good text for a graduate or an advanced undergraduate course. … Altogether, this is a very useful book for anyone interested in learning Bayesian networks without tears." (Jayanta K. Ghosh, International Statistical Reviews, Vol. 76 (2), 2008)"This book is the second edition of Jensen’s Bayesian Networks and Decision Graphs … . Each chapter ends with a summary section, bibliographic notes, and exercises. … provides a readable, self-contained, and above all, practical introduction to Bayesian networks and decision graphs. Its treatment is appropriate not just for statisticians, but also for computer scientists, engineers, and others researchers with appropriate mathematical background. … highly recommend it as a text or a useful reference for anyone interested in probabilistic graphical models or decision graphs." (Alyson G. Wilson, Journal of the American Statistical Association, Vol. 104 (485), March, 2009)“Devoted to Bayesian Networks or Graphical Models and Influence Diagrams, covering a full course with nice exercises … . It is useful as a reference for special topics. … strongly recommended for readers or user of BNs who are interested in specifying dependency models. … great importance to practitioners who try to find causality behind call-backs of products or crashes. … the book can be recommended to anybody working on the interface of operations research, AI, statistics and computer science.”­­­ (Hans-J. Lenz, Statistical Papers, Vol. 52, 2011)Table of ContentsCausal and Bayesian Networks * Part I: A Practical Guide to Normative Systems: Building Models * Learning, Adaptation, and Tuning * Decision Graphs * Part II: Algorithms for Normative Systems: Belief Updating in Bayesian Networks * Bayesian Network Analysis Tools * Algorithms for Influence Diagrams

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Book SynopsisKosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods.Trade ReviewFrom the reviews:"Introduction to Empirical Processes and Semiparametric Inference is a very good combination of both the empirical processes and semiparametric theories. This is the first book of its kind....I agree with the author that this book is 'more of a textbook than a research monograph.' As the semiparametric inference is currently an extremely active research area in statistical research, the book will open the door for graduate students to identify significant future research potentials. In fact, this book contains the author's newest research result, the application of semiparametric method in microarray data analysis. This book can be used as a textbook for graduate students in statistics, biostatistics, and economics (econometrics). In fact, the contents of this book can be tailored for different courses.""Generally, this is a great book on empirical processes and semiparametric methods. It should be on the must-read list for a serious statistician, biostatistician, or econometrician." (Biometrics, September 2008)"The main focus of this book is to introduce empirical processes and semiparametric inference methods to researchers interested in developing inferential tools for relatively complicated mathematical or statistical modeling problems. ...The material is structured in a sensible way supporting the learning and understanding of useful and challenging techniques of empirical processes and semiparametric inference. The book could well be very helpful for those studying and applying these techniques." (International Statistical Review 2008,77,2)“This book is an introduction to what is commonly called the modern theory of empirical processes – empirical processes indexed by classes of functions – and to semiparametric inference, and the interplay between both fields. … This is clearly intended to be a book for the novice in empirical process theory and semiparametric inference. … The main material is presented in a clearly arranged and logical order. … will be useful to anybody who wants to learn about the modern theory of empirical processes and semiparametric inference.” (Erich Häusler, Zentralblatt MATH, Vol. 1180, 2010)Table of ContentsOverview.- An Overview of Empirical Processes.- Overview of Semiparametric Inference.- Case Studies I.- Empirical Processes.- to Empirical Processes.- Preliminaries for Empirical Processes.- Stochastic Convergence.- Empirical Process Methods.- Entropy Calculations.- Bootstrapping Empirical Processes.- Additional Empirical Process Results.- The Functional Delta Method.- Z-Estimators.- M-Estimators.- Case Studies II.- Semiparametric Inference.- to Semiparametric Inference.- Preliminaries for Semiparametric Inference.- Semiparametric Models and Efficiency.- Efficient Inference for Finite-Dimensional Parameters.- Efficient Inference for Infinite-Dimensional Parameters.- Semiparametric M-Estimation.- Case Studies III.

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Book SynopsisMatrices.- Submatrices and Partitioned Matrices.- Linear Dependence and Independence.- Linear Spaces: Row and Column Spaces.- Trace of a (Square) Matrix.- Geometrical Considerations.- Linear Systems: Consistency and Compatibility.- Inverse Matrices.- Generalized Inverses.- Idempotent Matrices.- Linear Systems: Solutions.- Projections and Projection Matrices.- Determinants.- Linear, Bilinear, and Quadratic Forms.- Matrix Differentiation.- Kronecker Products and the Vec and Vech Operators.- Intersections and Sums of Subspaces.- Sums (and Differences) of Matrices.- Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraints.- The Moore-Penrose Inverse.- Eigenvalues and Eigenvectors.- Linear Transformations.- Erratum.Trade ReviewFrom a review: THE AUSTRALIAN AND NEW ZEALAND JOURNAL OF STATISTICS "This is a book that will be welcomed by many statisticians at most stages of professional development. ...It is essentially a carefully sequenced and tightly interlocking collections of proofs in an elementary, though very pure mathematical style." Table of ContentsPreface. - Matrices. - Submatrices and partitioned matricies. - Linear dependence and independence. - Linear spaces: row and column spaces. - Trace of a (square) matrix. - Geometrical considerations. - Linear systems: consistency and compatability. - Inverse matrices. - Generalized inverses. - Indepotent matrices. - Linear systems: solutions. - Projections and projection matrices. - Determinants. - Linear, bilinear, and quadratic forms. - Matrix differentiation. - Kronecker products and the vec and vech operators. - Intersections and sums of subspaces. - Sums (and differences) of matrices. - Minimzation of a second-degree polynomial (in n variables) subject to linear constraints. - The Moore-Penrose inverse. - Eigenvalues and Eigenvectors. - Linear transformations. - References. - Index.

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Book SynopsisLimitations of Linear Regression Applied on Ecological Data.- Things are not Always Linear; Additive Modelling.- Dealing with Heterogeneity.- Mixed Effects Modelling for Nested Data.- Violation of Independence Part I.- Violation of Independence Part II.- Meet the Exponential Family.- GLM and GAM for Count Data.- GLM and GAM for AbsencePresence and Proportional Data.- Zero-Truncated and Zero-Inflated Models for Count Data.- Generalised Estimation Equations.- GLMM and GAMM.- Estimating Trends for Antarctic Birds in Relation to Climate Change.- Large-Scale Impacts of Land-Use Change in a Scottish Farming Catchment.- Negative Binomial GAM and GAMM to Analyse Amphibian Roadkills.- Additive Mixed Modelling Applied on Deep-Sea Pelagic Bioluminescent Organisms.- Additive Mixed Modelling Applied on Phytoplankton Time Series Data.- Mixed Effects Modelling Applied on American Foulbrood Affecting Honey Bees Larvae.- Three-Way Nested Data for Age Determination Techniques Applied to Cetaceans.- GLTrade ReviewFrom the reviews:"For many people dealing with statistics is like jumping into ice-cold water. This metaphor is depicted by the cover of this book … . full of excellent example code and for most graphs and analyses the code is printed and explained in detail. … Each example finishes with … valuable information for a person new to a technique. In summary, I highly recommend the book to anyone who is familiar with basic statistics … who wants to expand his/her statistical knowledge to analyse ecological data." (Bernd Gruber, Basic and Applied Ecology, Vol. 10, 2009)"This book is written in a very approachable conversational style. The additional focus on the heuristics of the process rather than just a rote recital of theory and equations is commendable. This type of approach helps the reader get behind the ‘why’ of what’s being done rather than blindly follow a simple list of rules.… In short, this text is good for researchers with at least a little familiarity with the basic concepts of modeling and who want some solid stop-by-stop guidance with examples on how common ecological modeling tasks are accomplished using R." (Aaron Christ, Journal of Statistical Software, November 2009, Vol. 32)"The authors succeed in explaining complex extensions of regression in largely nonmathematical terms and clearly present appropriate R code for each analysis. A major strength of the text is that instead of relying on idealized datasets … the authors use data from consulting projects or dissertation research to expose issues associated with ‘real’ data. … The book is well written and accessible … . the volume should be a useful reference for advanced graduate students, postdoctoral researchers, and experienced professionals working in the biological sciences." (Paul E. Bourdeau, The Quarterly Review of Biology, Vol. 84, December, 2009)“This is a companion volume to Analyzing Ecology Data by the same authors. …It extends the previous work by looking at more complex general and generalized linear models involving mixed effects or heterogeneity in variances. It is aimed at statistically sophisticated readers who have a good understanding of multiple regression models… .The pedagogical style is informal… . The authors are pragmatists—they use combinations of informal graphical approaches, formal hypothesis testing, and information-theoretical model selection methods when analyzing data. …Advanced graduate students in ecology or ecologists with several years of experience with ‘messy’ data would find this book useful. …Statisticians would find this book interesting for the nice explorations of many of the issues with messy data. This book would be (very) suitable for a graduate course on statistical consulting—indeed, students would learn a great deal about the use of sophisticated statistical models in ecology! …I very much liked this book (and also the previous volume). I enjoyed the nontechnical presentations of the complex ideas and their emphasis that a good analysis uses ‘simple statistical methods wherever possible, but doesn’t use them simplistically.’” (Biometrics, Summer 2009, 65, 992–993)“This book is a great introduction to a wide variety of regression models. … This text examines how to fit many alternative models using the statistical package R. … The text is a valuable reference … . A large number of real datasets are used as examples. Discussion on which model to use and the large number of recent references make the book useful for self study … .” (David J. Olive, Technometrics, Vol. 52 (4), November, 2010)Table of ContentsLimitations of linear regression applied on ecological data. - Things are not always linear; additive modelling. - Dealing with hetergeneity. - Mixed modelling for nested data. - Violation of independence - temporal data. - Violation of independence; spatial data. - Generalised linear modelling and generalised additive modelling. - Generalised estimation equations. - GLMM and GAMM. - Estimating trends for Antarctic birds in relation to climate change. - Large-scale impacts of land-use change in a Scottish farming catchment. - Negative binomial GAM and GAMM to analyse amphibian road killings. - Additive mixed modelling applied on deep-sea plagic bioluminescent organisms. - Additive mixed modelling applied on phyoplankton time series data. - Mixed modelling applied on American Fouldbrood affecting honey bees larvae. - Three-way nested data for age determination techniques applied to small cetaceans. - GLMM applied on the spatial distribution of koalas in a fragmented landscape. - GEE and GLMM applied on binomial Badger activity data.

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Book SynopsisOnce the model has been introduced it is used to generate synthetic data, using R code, and these generated data are then used to estimate its parameters. This sequence enhances understanding of both the time series model and the R function used to fit the model to data.Trade ReviewFrom the reviews:“The book…gives a very broad and practical overview of the most common models for time series analysis in the time domain and in the frequency domain, with emphasis on how to implement them with base R and existing R packages such as Rnlme, MASS, tseries, fracdiff, mvtnorm, vars, and sspir. The authors explain the models by first giving a basic theoretical introduction followed by simulation of data from a particular model and fitting the latter to the simulated data to recover the parameters. After that, they fit the class of models to either environmental, finance, economics, or physics data. There are many applications to climate change and oceanography. The R programs for the simulations are given even if there are R functions that would do the simulation. All examples given can be reproduced by the reader using the code provided…in all chapters. Exercises at the end of each chapter are interesting, involving simulation, estimation, description, graphical analysis, and some theory. Data sets used throughout the book are available in a web site or come with base R or the R packages used. The book is a great guide to those wishing to get a basic introduction to modern time series modeling in practice, and in a short amount of time. …” (Journal of Statistical Software, January 2010, Vol. 32, Book Review 4)“Later year undergraduates, beginning graduate students, and researchers and graduate students in any discipline needing to explore and analyse time series data. This very readable text covers a wide range of time series topics, always however within a theoretical framework that makes normality assumptions. The range of models that are discussed is unusually wide for an introductory text. … The mathematical theory is remarkably complete … . This text is recommended for its wide-ranging and insightful coverage of time series theory and practice.” (John H. Maindonald, International Statistical Review, Vol. 78 (3), 2010)“The authors present a textbook for students and applied researchers for time series analysis and linear regression analysis using R as the programming and command language. … The book is written for students with knowledge of a first-year university statistics course in New-Zealand and Australia, but it also might serve as a useful tools for applied researchers interested in empirical procedures and applications which are not menu driven as it is the case for most econometric software packages nowadays.” (Herbert S. Buscher, Zentralblatt MATH, Vol. 1179, 2010)Table of ContentsTime Series Data.- Correlation.- Forecasting Strategies.- Basic Stochastic Models.- Regression.- Stationary Models.- Non-stationary Models.- Long-Memory Processes.- Spectral Analysis.- System Identification.- Multivariate Models.- State Space Models.

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Book SynopsisDifferentiable Dynamical Systems.- Notes.- References for Notes.- What Is Global Analysis?.- Stability and Genericity in Dynamical Systems.- Personal Perspectives on Mathematics and Mechanics.- Dynamics in General Equilibrium Theory.- Some Dynamical Questions in Mathematical Economics.- Review of Global Variational Analysis: Weier strass Integrals on a Riemannian Manifold.- Review of Catastrophe Theory: Selected Papers.- On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff.- Robert Edward Bowen (jointly with J. Feldman and M. Ratner).- On How I Got Started in Dynamical Systems.Table of ContentsDifferentiable Dynamical Systems.- Notes.- References for Notes.- What Is Global Analysis?.- Stability and Genericity in Dynamical Systems.- Personal Perspectives on Mathematics and Mechanics.- Dynamics in General Equilibrium Theory.- Some Dynamical Questions in Mathematical Economics.- Review of Global Variational Analysis: Weier strass Integrals on a Riemannian Manifold.- Review of Catastrophe Theory: Selected Papers.- On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff.- Robert Edward Bowen (jointly with J. Feldman and M. Ratner).- On How I Got Started in Dynamical Systems.

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Book SynopsisGetting Data into R.- Accessing Variables and Managing Subsets of Data.- Simple Functions.- An Introduction to Basic Plotting Tools.- Loops and Functions.- Graphing Tools.- An Introduction to the Lattice Package.- Common R Mistakes.Trade ReviewFrom the reviews:“A Beginner’s Guide to R is just what its title implies, a quick-start guide for the newest R users. A unique feature of this welcome addition to Springer’s Use R! series is that it is devoted solely to getting the user up and running on R. Unlike other texts geared towards R beginners, …this text does not make the mistake of trying to simultaneously teach statistics. …there are straightforward homework exercises provided throughout…, and the data sets can be downloaded from the authors’ website… …A Beginner’s Guide to R is an essential resource for the R novice, whether an undergraduate learning statistics for the first time or a seasoned statistician biting the bullet and making the switch to R. “ (The R Journal Vol. 2/1, June 2010)“…most suitable for an advanced beginner or a user who needs an introduction to a wide variety of graphical methods. Overall, the book does most things quite well. It shows the beginner how to install R. how to load data into R, how to perform some subsetting operations including the sorting of data and most of all how to plot data using a variety of methods. Throughout, all methods and code are will illustrated and can be easily replicated by anyone using the book. …I learned quite a number of things about R that I did not previously know. Consequently, I would recommend the book not only for the students who need to learn R, but for professionals who need to enhance their basic working knowledge of R." (Math Geosci 2010, 42: 133–137)“The book has many admirable features. It introduces key commands in easy stages. Each chapter has a number of illustrative examples, lucidly explained, and ends with a review of what has been covered. Chapters also contain exercises at the end that reinforce the examples provided. … useful work for self-study or for an introductory course, allowing readers to apply their knowledge of the language to begin learning how to use R for statistical analysis or other purposes. Summing Up: Highly recommended. All levels of readership.” (R. Bharath, Choice, Vol. 47 (11), July, 2010)“This book explains how to create datasets, variables, functions and plots using R. It is not a simple book though. … somewhat dense and covers each topic thoroughly. … best to follow every example. … I found this book to be well written for its intended audience and purpose. I had no difficulty reading it or following the examples. … This approach will give you a good foundation for using R in your own work and advancing to other books about specific analyses and procedures.” (Mark Bailey, Technometrics, Vol. 53 (1), February, 2011)“This book has a very clear objective. … this is a popular book about the R statistical software. … The book is true to its goal of being a text for the absolute beginner with easy to follow explanations, examples to program, and exercises to build skill. The reader who takes advantages of the available data files and R text editors will find this to be a very instructive book. It will definitely increase your desire to learn and use R in the future.” (Brandon Alleman, The American Statistician, May, 2011)Table of ContentsGetting Data into R.- Accessing Variables and Managing Subsets of Data.- Simple Functions.- An Introduction to Basic Plotting Tools.- Loops and Functions.- Graphing Tools.- An Introduction to the Lattice Package.- Common R Mistakes.

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Book Synopsis1: Cars, Goats, and Sample Spaces. 2: How to Count: Birthdays andLotteries. 3: Conditional Probability: From Kings to Prisoners. 4: TheFormula of Thomas Bayes and Other Matters. 5: The Idea ofIndependence, with Applications. 6: A Little Bit About Games. 7:Random Variables, Expectations, and More About Games. 8: BaseballCards, The Law of Large Numbers, and Bad News for Gamblers. 9: FromTraffic to Chocolate Chip Cookies with the Poisson Distribution. 10:The Desperate Case of the Gambler's Ruin. 11: Breaking Sticks, TossingNeedles, and More: Probability on Continuous Sample Spaces. 12: NormalDistribution, and Order from Diversity via the Central Limit Theorem.13: Random Numbers: What They Are and How to Use Them. 14: Computersand Probability. 15: Statistics: Applying Probability to MakeDecisions. 16: Roaming the Number Line with a Markov Chain:Dependence. 17: The Brownian Motion, and Other Processes in ContinuousTime.Table of Contents1 Cars, Goats, and Sample Spaces.- 1.1 Getting your goat.- 1.2 Nutshell history and philosophy lesson.- 1.3 Let those dice roll. Sample spaces.- 1.4 Discrete sample spaces. Probability distributions and spaces.- 1.5 The car-goat problem solved.- 1.6 Exercises for Chapter 1.- 2 How to Count: Birthdays and Lotteries.- 2.1 Counting your birthdays.- 2.2 Following your dreams in Lottoland.- 2.3 Exercises for Chapter 2.- 3 Conditional Probability: From Kings to Prisoners.- 3.1 Some probability rules. Conditional Probability.- 3.2 Does the king have a sister?.- 3.3 The prisoner’s dilemma.- 3.4 All about urns.- 3.5 Exercises for Chapter 3.- 4. The Formula of Thomas Bayes and Other Matters.- 4.1 On blood tests and Bayes’s formula.- 4.2 An urn problem.- 4.3 Laplace’s law of succession.- 4.4 Subjective probability.- 4.5 Questions of paternity.- 4.6 Exercises for Chapter 4.- 5 The Idea of Independence, with Applications.- 5.1 Independence of events.- 5.2 Waiting for the first head to show.- 5.3 On the likelihood of alien life.- 5.4 The monkey at the typewriter.- 5.5 Rare events do occur.- 5.6 Rare versus extraordinary events.- 5.7 Exercises for Chapter 5.- 6 A Little Bit About Games.- 6.1 The problem of points.- 6.2 Craps.- 6.3 Roulette.- 6.4 What are the odds?.- 6.5 Exercises for Chapter 6.- 7 Random Variables, Expectations, and More About Games.- 7.1 Random variables.- 7.2 The binomial random variable.- 7.3 The game of chuck-a-luck and de Méré’s problem of dice.- 7.4 The expectation of a random variable.- 7.5 Fair and unfair games.- 7.6 Gambling systems.- 7.7 Administering a blood test.- 7.8 Exercises for Chapter 7.- 8 Baseball Cards, The Law of Large Numbers, and Bad News for Gamblers.- 8.1 The coupon collector’s problem.- 8.2 Indicator variables and the expectation of a binomial variable.- 8.3 Independent random variables.- 8.4 The coupon collector’s problem solved.- 8.5 The Law of Large Numbers.- 8.6 The Law of Large Numbers and gambling.- 8.7 A gambler’s fallacy.- 8.8 The variance of a random variable.- 8.8.1 Appendix.- 8.8.2 The variance of the sum of independent random variables.- 8.8.3 The variance ofSn/n.- 8.9 Exercises for Chapter 8.- 9 From Traffic to Chocolate Chip Cookies with the Poisson Distribution.- 9.1 A traffic problem.- 9.2 The Poisson as an approximation to the binomial.- 9.3 Applications of the Poisson distribution.- 9.4 The Poisson process.- 9.5 Exercises for Chapter 9.- 10 The Desperate Case of the Gambler’s Ruin.- 10.1 Let’s go for a random walk.- 10.2 The gambler’s ruin problem.- 10.3 Bold play or timid play?.- 10.4 Exercises for Chapter 10.- 11 Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces.- 11.1 Choosing a number at random from an interval.- 11.2 Bus stop.- 11.3 The expectation of a continuous random variable.- 11.4 Normal numbers.- 11.5 Bertrand’s paradox.- 11.6 When do we have a triangle?.- 11.7 Buffon’s needle problem.- 11.8 Exercises for Chapter 11.- 12 Normal Distributions, and Order from Diversity via the Central Limit Theorem.- 12.1 Making sense of some data.- 12.2 The normal distributions.- 12.3 Some pleasant properties of normal distributions.- 12.4 The Central Limit Theorem.- 12.5 How many heads did you get?.- 12.6 Why so many quantities may be approximately normal.- 12.7 Exercises for Chapter 12.- 13 Random Numbers: What They Are and How to Use Them.- 13.1 What are random numbers?.- 13.2 When are digits random? Statistical randomness.- 13.3 Pseudo-random numbers.- 13.4 Random sequences arising from decimal expansions.- 13.5 The use of random numbers.- 13.6 The 1970 draft lottery.- 13.7 Exercises for Chapter 13.- 14 Computers and Probability.- 14.1 A little bit about computers.- 14.2 Frequency of zeros in a random sequence.- 14.3 Simulation of tossing a coin.- 14.4 Simulation of rolling a pair of dice.- 14.5 Simulation of the Buffon needle tosses.- 14.6 Monte Carlo estimate of ? using bombardment of a circle.- 14.7 Monte Carlo estimate for the broken stick problem.- 14.8 Monte Carlo estimate of a binomial probability.- 14.9 Monte Carlo estimate of the probability of winning at craps.- 14.10 Monte Carlo estimate of the gambler’s ruin probability.- 14.11 Constructing approximately normal random variables.- 14.12 Exercises for Chapter 14.- 15 Statistics: Applying Probability to Make Decisions.- 15.1 What statistics does.- 15.2 Lying with statistics?.- 15.3 Deciding between two probabilities.- 15.4 More complicated decisions.- 15.5 How many fish in the lake, and other problems of estimation.- 15.6 Polls and confidence intervals.- 15.7 Random sampling.- 15.8 Some concluding remarks.- 15.9 Exercises for Chapter 15.- 16 Roaming the Number Line with a Markov Chain: Dependence.- 16.1 A picnic in Alphaville?.- 16.2 One-dimensional random walks.- 16.3 The probability of ever returning “home”.- 16.4 About the gambler recouping her losses.- 16.5 The dying out of family names.- 16.6 The number of parties waiting for a taxi.- 16.7 Stationary distributions.- 16.8 Applications to genetics.- 16.9 Exercises for Chapter 16.- 17 The Brownian Motion, and Other Processes in Continuous Time.- 17.1 Processes in continuous time.- 17.2 A few computations for the Poisson process.- 17.3 The Brownian motion process.- 17.4 A few computations for Brownian motion.- 17.5 Brownian motion as a limit of random walks.- 17.6 Exercises for Chapter 17.- Answers to Exercises.

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Book SynopsisI: The Dichotomous Rasch Model.- 1. Some Background for Item Response Theory and the Rasch Model.- 2. Derivations of the Rasch Model.- 3. Estimation of Item Parameters.- 4. On Person Parameter Estimation in the Dichotomous Rasch Model.- 5. Testing the Rasch Model.- 6. The Assessment of Person Fit.- 7. Test Construction from Item Banks.- II: Extensions of the Dichotomous Rasch Model.- 8. The Linear Logistic Test Model.- 9. Linear Logistic Models for Change.- 10. Dynamic Generalizations of the Rasch Model.- 11. Linear and Repeated Measures Models for the Person Parameters.- 12. The One Parameter Logistic Model.- 13. Linear Logistic Latent Class Analysis and the Rasch Model.- 14. Mixture Distribution Rasch Models.- III: Polytomous Rasch Models and their Extensions.- 15. Polytomous Rasch Models and their Estimation.- 16. The Derivation of Polytomous Rasch Models.- 17. The Polytomous Rasch Model within the Class of Generalized Linear Symmetry Models.- 18. Tests of Fit for Polytomous Rasch MTable of ContentsI: The Dichotomous Rasch Model.- 1. Some Background for Item Response Theory and the Rasch Model.- 2. Derivations of the Rasch Model.- 3. Estimation of Item Parameters.- 4. On Person Parameter Estimation in the Dichotomous Rasch Model.- 5. Testing the Rasch Model.- 6. The Assessment of Person Fit.- 7. Test Construction from Item Banks.- II: Extensions of the Dichotomous Rasch Model.- 8. The Linear Logistic Test Model.- 9. Linear Logistic Models for Change.- 10. Dynamic Generalizations of the Rasch Model.- 11. Linear and Repeated Measures Models for the Person Parameters.- 12. The One Parameter Logistic Model.- 13. Linear Logistic Latent Class Analysis and the Rasch Model.- 14. Mixture Distribution Rasch Models.- III: Polytomous Rasch Models and their Extensions.- 15. Polytomous Rasch Models and their Estimation.- 16. The Derivation of Polytomous Rasch Models.- 17. The Polytomous Rasch Model within the Class of Generalized Linear Symmetry Models.- 18. Tests of Fit for Polytomous Rasch Models.- 19. Extended Rating Scale and Partial Credit Models for Assessing Change.- 20. Polytomous Mixed Rasch Models.- In Retrospect.- 21. What Georg Rasch Would Have Thought about this Book.- References.- Author Index.- Abbreviations.

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Book SynopsisThe aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D.Trade ReviewFrom the reviews: "Another excellent book in theory of statistics is by Mark J. Schervish. … Readers will enjoy reading this book to see how differently the theory can be presented … . This well written book contains nine chapters and four appendices. ... Each chapter has both easy and challenging problems. The book is suitable for graduate level statistical theory courses. Examples and illustrations are well explained. I liked the author’s presentation, and learned a lot from the book. I highly recommend this book to theoretical statisticians." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 74 (11), November, 2004)Table of ContentsContent.- 1: Probability Models.- 1.1 Background.- 1.1.1 General Concepts.- 1.1.2 Classical Statistics.- 1.1.3 Bayesian Statistics.- 1.2 Exchangeability.- 1.2.1 Distributional Symmetry.- 1.2.2 Frequency arid Exchangeability.- 1.3 Parametric Models.- 1.3.1 Prior, Posterior, and Predictive Distributions.- 1.3.2 Improper Prior Distributions.- 1.3.3 Choosing Probability Distributions.- 1.4 DeFinetti’s Representation Theorem.- 1.4.1 Understanding the Theorems.- 1.4.2 The Mathematical Statements.- 1.4.3 Some Examples.- 1.5 Proofs of DeFinetti’s Theorem and Related Results*.- 1.5.1 Strong Law of Large Numbers.- 1.5.2 The Bernoulli Case.- 1.5.3 The General Finite Case*.- 1.5.4 The General Infinite Case.- 1.5.5 Formal Introduction to Parametric Models*.- 1.6 Infinite-Dimensional Parameters*.- 1.6.1 Dirichlet Processes.- 1.6.2 Tailfree Processes+.- 1.7 Problems.- 2: Sufficient Statistics.- 2.1 Definitions.- 2.1.1 Notational Overview.- 2.1.2 Sufficiency.- 2.1.3 Minimal and Complete Sufficiency.- 2.1.4 Ancillarity.- 2.2 Exponential Families of Distributions.- 2.2.1 Basic Properties.- 2.2.2 Smoothness Properties.- 2.2.3 A Characterization Theorem*.- 2.3 Information.- 2.3.1 Fisher Information.- 2.3.2 Kullback-Leibler Information.- 2.3.3 Conditional Information*.- 2.3.4 Jeffreys’ Prior*.- 2.4 Extremal Families*.- 2.4.1 The Main Results.- 2.4.2 Examples.- 2.4.3 Proofs+.- 2.5 Problems.- Chapte 3: Decision Theory.- 3.1 Decision Problems.- 3.1.1 Framework.- 3.1.2 Elements of Bayesian Decision Theory.- 3.1.3 Elements of Classical Decision Theory.- 3.1.4 Summary.- 3.2 Classical Decision Theory.- 3.2.1 The Role of Sufficient Statistics.- 3.2.2 Admissibility.- 3.2.3 James—Stein Estimators.- 3.2.4 Minimax Rules.- 3.2.5 Complete Classes.- 3.3 Axiomatic Derivation of Decision Theory*.- 3.3.1 Definitions and Axioms.- 3.2.2 Examples.- 3.3.3 The Main Theorems.- 3.3.4 Relation to Decision Theory.- 3.3.5 Proofs of the Main Theorems*.- 3.3.6 State-Dependent Utility*.- 3.4 Problems.- 4: Hypothesis Testing.- 4.1 Introduction.- 4.1.1 A Special Kind of Decision Problem.- 4.1.2 Pure Significance Tests.- 4.2 Bayesian Solutions.- 4.2.1 Testing in General.- 4.2.2 Bayes Factors.- 4.3 Most Powerful Tests.- 4.3.1 Simple Hypotheses and Alternatives.- 4.3.2 Simple Hypotheses, Composite Alternatives.- 4.3.3 One-Sided Tests.- 4.3.4 Two-Sided Hypotheses.- 4.4 Unbiased Tests.- 4.4.1 General Results.- 4.4.2 Interval Hypotheses.- 4.4.3 Point Hypotheses.- 4.5 Nuisance Parameters.- 4.5.1 Neyinan Structure.- 4.5.2 Tests about Natural Parameters.- 4.5.3 Linear Combinations of Natural Parameters.- 4.5.4 Other Two-Sided Cases*.- 4.5.5 Likelihood Ratio Tests.- 4.5.6 The Standard F-Test as a Bayes Rule.- 4.6 P-Values.- 4.6.1 Definitions and Examples.- 4.6.2 P-Values and Bayes Factors.- 4.7 Problems.- 5: Estimation.- 5.1 Point Estimation.- 5.1.1 Minimum Variance Unbiased Estimation.- 5.1.2 Lower Bounds on the Variance of Unbiased Estimators.- 5.1.3 Maximum Likelihood Estimation.- 5.1.4 Bayesian Estimation.- 5.1.5 Robust Estimation*.- 5.2 Set Estimation.- 5.2.1 Confidence Sets.- 5.2.2 Prediction Sets*.- 5.2.3 Tolerance Sets*.- 5.2.4 Bayesian Set Estimation.- 5.2.5 Decision Theoretic Set Estimation.- 5.3 The Bootstrap*.- 5.3.1 The General Concept.- 5.3.2 Standard Deviations and Bias.- 5.3.3 Bootstrap Confidence Intervals.- 5.4 Problems.- 6: Equivariance*.- 6.1 Common Examples.- 6.1.1 Location Problems.- 6.1.2 Scale Problems.- 6.2 Equivariant Decision Theory.- 6.2.1 Groups of Transformations.- 6.2.2 Equivariance and Changes of Units.- 6.2.3 Minimum Risk Equivariant Decisions.- 6.3 Testing and Confidence Intervals*.- 6.3.1 P-Values in Invariant Problems.- 6.3.2 Equivariant Confidence Sets.- 6.3.3 Invariant Tests*.- 6.4 Problems.- 7: Large Sample Theory.- 7.1 Convergence Concepts.- 7.1.1 Deterministic Convergence.- 7.1.2 Stochastic Convergence.- 7.1.3 The Delta Method.- 7.2 Sample Quantiles.- 7.2.1 A Single Quantile.- 7.2.2 Several Quantiles.- 7.2.3 Linear Combinations of Quantiles*.- 7.3 Large Sample Estimation.- 7.3.1 Some Principles of Large Sample Estimation.- 7.3.2 Maximum Likelihood Estimators.- 7.3.3 MLEs in Exponential Families.- 7.3.4 Examples of Inconsistent MLEs.- 7.3.5 Asymptotic Normality of MLEs.- 7.3.6 Asymptotic Properties of M-Estimators.- 7.4 Large Sample Properties of Posterior Distributions.- 7.4.1 Consistency of Posterior Distributions+.- 7.4.2 Asymptotic Normality of Posterior Distributions.- 7.4.3 Laplace Approximations to Posterior Distributions*.- 7.4.4 Asymptotic Agreement of Predictive Distributions+.- 7.5 Large Sample Tests.- 7.5.1 Likelihood Ratio Tests.- 7.5.2 Chi-Squarcd Goodness of Fit Tests.- 7.6 Problems.- 8: Hierarchical Models.- 8.1 Introduction.- 8.1.1 General Hierarchical Models.- 8.1.2 Partial Exchangeability*.- 8.1.3 Examples of the Representation Theorem*.- 8.2 Normal Linear Models.- 8.2.1 One-Way ANOVA.- 8.2.2 Two-Way Mixed Model ANOVA*.- 8.2.3 Hypothesis Testing.- 8.3 Nonnormal Models*.- 8.3.1 Poisson Process Data.- 8.3.2 Bernoulli Process Data.- 8.4 Empirical Bayes Analysis*.- 8.4.1 Naïve Empirical Bayes.- 8.4.2 Adjusted Empirical Bayes.- 8.4.3 Unequal Variance Case.- 8.5 Successive Substitution Sampling.- 8.5.1 The General Algorithm.- 8.5.2 Normal Hierarchical Models.- 8.5.3 Nonnormal Models.- 8.6 Mixtures of Models.- 8.6.1 General Mixture Models.- 8.6.2 Outliers.- 8.6.3 Bayesian Robustness.- 8.7 Problems.- 9: Sequential Analysis.- 9.1 Sequential Decision Problems.- 9.2 The Sequential Probability Ratio Test.- 9.3 Interval Estimation*.- 9.4 The Relevancc of Stopping Rules.- 9.5 Problems.- Appendix A: Measure and Integration Theory.- A.1 Overview.- A.1.1 Definitions.- A.1.2 Measurable Functions.- A.1.3 Integration.- A.1.4 Absolute Continuity.- A.2 Measures.- A.3 Measurable Functions.- A.4 Integration.- A.5 Product Spaces.- A.6 Absolute Continuity.- A.7 Problems.- Appendix B: Probability Theory.- B.1 Overview.- B.1.1 Mathematical Probability.- B.1.2 Conditioning.- B.1.3 Limit Theorems.- B.2 Mathematical Probability.- B.2.1 Random Quantities and Distributions.- B.2.2 Some Useful Inequalities.- B.3 Conditioning.- B.3.1 Conditional Expectations.- B.3.2 Borel Spaces*.- B.3.3 Conditional Densities.- B.3.4 Conditional Independence.- B.3.5 The Law of Total Probability.- B.4 Limit Theorems.- B.4.1 Convergence in Distribution and in Probability.- B.4.2 Characteristic Functions.- B.5 Stochastic Processes.- B.5.1 Introduction.- B.5.3 Markov Chains*.- B.5.4 General Stochastic Processes.- B.6 Subjective Probability.- B.7 Simulation*.- B.8 Problems.- Appendix C: Mathematical Theorems Not Proven Here.- C.1 Real Analysis.- C.2 Complex Analysis.- C.3 Functional Analysis.- Appendix D: Summary of Distributions.- D.1 Univariate Continuous Distributions.- D.2 Univariate Discrete Distributions.- D.3 Multivariate Distributions.- References.- Notation and Abbreviation Index.- Name Index.

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