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

This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables.
- Covers a wide class of important models
- Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data
- Includes illustrative examples with real data sets from business, education, medicine, public health and sociology.
- Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.

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

This book brings together important topics of current research in probabilistic graphical modeling, learning from data and probabilistic inference. Coverage includes such topics as the characterization of conditional independence, the learning of graphical models with latent variables, and extensions to the influence diagram formalism as well as important application fields, such as the control of vehicles, bioinformatics and medicine.

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

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

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

Analyzing observed or measured data is an important step in applied sciences. The recent increase in computer capacity has resulted in a revolution both in data collection and data analysis. An increasing number of scientists, researchers and students are venturing into statistical data analysis; hence the need for more guidance in this field, which was previously dominated mainly by statisticians.

This handbook fills the gap in the range of textbooks on data analysis. Written in a dictionary format, it will serve as a comprehensive reference book in a rapidly growing field. However, this book is more structured than an ordinary dictionary, where each entry is a separate, self-contained entity. The authors provide not only definitions and short descriptions, but also offer an overview of the different topics. Therefore, the handbook can also be used as a companion to textbooks for undergraduate or graduate courses.

1700 entries are given in alphabetical order grouped into 20 topics and each topic is organized in a hierarchical fashion. Additional specific entries on a topic can be easily found by following the cross-references in a top-down manner. Several figures and tables are provided to enhance the comprehension of the topics and a list of acronyms helps to locate the full terminologies. The bibliography offers suggestions for further reading.

This volume collects a selection of refereed papers of the more than one hundred presented at the InternationalConference MAF 2008 - Mathematicaland Statistical Methods for Actuarial Sciences and Finance. The conference was organised by the Department of Applied Mathematics and theDepartment ofStatisticsoftheUniversityCa'Foscari Venice(Italy), withthec- laborationofthe Department ofEconomics and StatisticalSciences ofthe University ofSalerno(Italy).Itwas heldinVenice, fromMarch 26to28,2008, attheprestigious CavalliFranchettipalace, alongGrand Canal, oftheIstitutoVenetodiScienze, Lettere ed Arti. This conference was the ?rst international edition of a biennial national series begunin2004, whichwas bornof thebrilliantbeliefofthe colleagues -and friends- oftheDepartmentofEconomicsandStatisticalSciences oftheUniversityofSalerno: the idea following which the cooperation between mathematicians and statisticians in working in actuarial sciences, in insurance and in ?nance can improve research on these topics. The proof of this consists in the wide participation in these events. In particular, with reference to the 2008 internationaledition: - More than 150 attendants, both academicians and practitioners; - More than 100 accepted communications, organised in 26 parallel sessions, from authors coming from about twenty countries (namely: Canada, Colombia, Czech Republic, France, Germany, Great Britain, Greece, Hungary, Ireland, Israel, Italy, Japan, Poland, Spain, Sweden, Switzerland, Taiwan, USA); - two plenary guest-organised sessions; and - aprestigiouskeynotelecturedeliveredbyProfessorWolfgangHa ]rdleoftheH- boldt Universityof Berlin (Germany)

This book lays the foundations for a theory on almost periodic stochastic processes and their applications to various stochastic differential equations, functional differential equations with delay, partial differential equations, and difference equations. It is in part a sequel of authors recent work on almost periodic stochastic difference and differential equations and has the particularity to be the first book that is entirely devoted to almost periodic random processes and their applications. The topics treated in it range from existence, uniqueness, and stability of solutions for abstract stochastic difference and differential equations.

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

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

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

Audience

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

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

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

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

The Author

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

The role of probability in computer science has been growing for years and, in lieu of a tailored textbook, many courses have employed a variety of similar, but not entirely applicable, alternatives. To meet the needs of the computer science graduate student (and the advanced undergraduate), best-selling author Sheldon Ross has developed the premier probability text for aspiring computer scientists involved in computer simulation and modeling. The math is precise and easily understood. As with his other texts, Sheldon Ross presents very clear explanations of concepts and covers those probability models that are most in demand by, and applicable to, computer science and related majors and practitioners.
Many interesting examples and exercises have been chosen to illuminate the techniques presented
Examples relating to bin packing, sorting algorithms, the find algorithm, random graphs, self-organising list problems, the maximum weighted independent set problem, hashing, probabilistic verification, max SAT problem, queuing networks, distributed workload models, and many othersMany interesting examples and exercises have been chosen to illuminate the techniques presented

This volume contains a collection of papers dedicated to Professor Eckhard Platen to celebrate his 60th birthday, which occurred in 2009. The contributions have been written by a number of his colleagues and co-authors. All papers have been - viewed and presented as keynote talks at the international conference "Quantitative Methods in Finance" (QMF) in Sydney in December 2009. The QMF Conference Series was initiated by Eckhard Platen in 1993 when he was at the Australian - tional University (ANU) in Canberra. Since joining UTS in 1997 the conference came to be organised on a much larger scale and has grown to become a signi?cant international event in quantitative ?nance. Professor Platen has held the Chair of Quantitative Finance at the University of Technology, Sydney (UTS) jointly in the Faculties of Business and Science since 1997. Prior to this appointment, he was the Founding Head of the Centre for Fin- cial Mathematics at the Institute of Advanced Studies at ANU, a position to which he was appointed in 1994. Eckhard completed a PhD in Mathematics at the Technical University in Dresden in 1975 and in 1985 obtained his Doctor of Science degree (Habilitation degree in the German system) from the Academy of Sciences in Berlin where he headed the Stochastics group at the Weierstrass Institute.

This volume investigates the notion of reduction. Building on the idea that philosophersemploy the term 'reduction' to reconcile diversity and directionality with unity, without relying on elimination, the book offers a powerful explication of an "ontological," notion of reduction the extension of which is (primarily) formed by properties, kinds, individuals, or processes. It argues that related notions of reduction, such as theory-reduction and functional reduction, should be defined in terms of this explication. Thereby, the book offers a coherent framework, which sheds light on the history of the various reduction debates in the philosophy of science and in the philosophy of mind, and on related topics such as reduction and unification, the notion of a scientific level, and physicalism.

The book takes its point of departure in the examination of a puzzle about reduction. To illustrate, the book takes as an example the reduction of water. If water reduces to H2O, then water is identical to H2O - thus we get unity. Unity does not come at the price of elimination - claiming that water reduces to H2O, we do not thereby claim that there is no water. But what about diversity and directionality? Intuitively, there should be a difference between water and H2O, such that we get diversity. This is required for there to be directionality: in a sense, if water reduces to H2O, then H2O is prior to, or more basic than water. At least, if water reduces to H2O, then H2O does not reduce to water. But how can this be, if water is identical to H2O? The book shows that the application of current models of reduction does not solve this puzzle, and proposes a new coherent definition, according to which unity is tied to identity, diversity is descriptive in nature, and directionality is the directionality of explanation."

Now more than ever, educators are being held accountable by taxpayers, students, parents, government officials and the business community for supportable documentation of educational results. Data management has become everyone's job and everyone's concern. But the egression of data has exposed a raw nerve. The lack of comfort that many educators have in working with data poses a great challenge as school districts make the transition from a data rich to an information rich environment. How to Become Data Literate is the solution. It is clear that educators need the ability to formulate and answer questions using data as part of evidence-based thinking, selecting and using appropriate data tools, interpreting information from data, evaluating evidence-based differences, using data to solve real problems and communicating solutions. This book is intended to be a user-friendly, educator's primer. It will leave the reader with the confident attitude that "I can do this." In the long run, it is intended to underscore the magnificence of data. Decisions based on excellent data produce meaningful action strategies that benefit students, parents, staff, and the community at large.

Geostatistics is a common tool in reservoir characterization. Written from the basics of statistics, this book covers only those topics that are needed for the two goals of the text: to exhibit the diagnostic potential of statistics and to introduce the important features of statistical modelling. This revised edition contains expanded discussions of some materials, in particular conditional probabilities, Bayes Theorem, correlation, and Kriging. The coverage of estimation, variability, and modelling applications have been updated. Seventy examples illustrate concepts and show the role of geology for providing important information for data analysis and model building. Four reservoir case studies conclude the presentation, illustrating the application and importance of the earlier material. This book aims to help petroleum professionals develop more accurate models, leading to lower sampling costs. It is an ideal book for petroleum engineers, geoscientists, hydrologists, and faculty and students in these and related fields.

This book presents basic aspects for a theory of statistics with fuzzy data, together with a set of practical applications. Theories of fuzzy logic and of random closed sets are used as basic ingredients in building statistical concepts and procedures in the context of imprecise data, including coarse data analysis. The book aims at motivating statisticians to examine fuzzy statistics to enlarge the domain of applicability of statistics in general.

Simulation is a controlled statistical sampling technique that can be used to study complex stochastic systems when analytic and/or numerical techniques do not suffice. The focus of this book is on simulations of discrete-event stochastic systems; namely, simulations in which stochastic state transitions occur only at an increasing sequence of random times. The discussion emphasizes simulations on a finite or countably infinite state space.
* Develops probabilistic methods for simulation of discrete-event stochastic systems
* Emphasizes stochastic modeling and estimation procedures based on limit theorems for regenerative stochastic processes
* Includes engineering applications of discrete-even simulation to computer, communication, manufacturing, and transportation systems
* Focuses on simulations with an underlying stochastic process that can specified as a generalized semi-Markov process
* Unique approach to simulation, with heavy emphasis on stochastic modeling
* Includes engineering applications for computer, communication, manufacturing, and transportation systems

Long-rangedependent, or long-memory,time seriesarestationarytime series displaying a statistically signi?cant dependence between very distant obs- vations. We formalize this dependence by assuming that the autocorrelation function of these stationary series decays very slowly, hyperbolically, as a function of the time lag. Many economic series display these empirical features: volatility of asset prices returns, future interest rates, etc. There is a huge statistical literature on long-memory processes, some of this research is highly technical, so that it is cited, but often misused in the applied econometrics and empirical e- nomics literature. The ?rst purpose of this book is to present in a formal and pedagogical way some statistical methods for studying long-range dependent processes. Furthermore, the occurrence of long-memory in economic time series might be a statistical artefact as the hyperbolic decay of the sample autoc- relation function does not necessarily derive from long-range dependent p- cesses. Indeed, the realizations of non-homogeneous processes, e.g., switching regime and change-point processes, display the same empirical features. We thus also present in this book recent statistical methods able to discriminate between the long-memory and change-point alternatives. Going beyond the purely statistical analysis of economic series, it is of interest to determine which economic mechanisms are generating the strong dependence properties of economic series, whether they are genuine, or spu- ous. The regularities of the long-memory and change-point properties across economic time series, e.g., common degree of long-range dependence and/or common change-points, suggest the existence of a common economic cause.

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

Thisbookisintendedformolecularbiologistswhoperformquantitativeanalysesondata emanatingfromtheir?eldandforthestatisticianswhoworkwithmolecularbiologists andotherbiomedicalresearchers. Therearemanyexcellenttextbooksthatprovidefun- mentalcomponentsforstatisticaltrainingcurricula. Therearealsomany"byexpertsfor experts"booksinstatisticsandmolecularbiologywhichrequirein-depthknowledgein bothsubjectstobetakenfulladvantageof. Sofar,nobookinstatisticshasbeenpublished thatprovidesthebasicprinciplesofproperstatisticalanalysesandprogressestoamore advancedstatisticsinresponsetorapidlydevelopingtechnologiesandmethodologiesin the?eldofmolecularbiology. Respondingtothissituation,ourbookaimsatbridgingthegapbetweenthesetwo extremes. Molecularbiologistswillbene?tfromtheprogressivestyleofthebookwhere basicstatisticalmethodsareintroducedandgraduallyelevatedtoanintermediatelevel. Similarly,statisticianswillbene?tfromlearningthevariousbiologicaldatageneratedfrom the?eldofmolecularbiology,thetypesofquestionsofinteresttomolecularbiologists, andthestatisticalapproachestoanalyzingthedata. Thestatisticalconceptsandmethods relevanttostudiesinmolecularbiologyarepresentedinasimpleandpracticalmanner. Speci?cally,thebookcoversbasicandintermediatestatisticsthatareusefulforclassical and molecular biology settings and advanced statistical techniques that can be used to helpsolveproblemscommonlyencounteredinmodernmolecularbiologystudies,such assupervisedandunsupervisedlearning,hiddenMarkovmodels,manipulationandan- ysisofdatafromhigh-throughputmicroarrayandproteomicplatform,andsynthesisof these evidences. A tutorial-type format is used to maximize learning in some chapters. Advicefromjournaleditorsonpeer-reviewedpublicationandsomeusefulinformationon softwareimplementationarealsoprovided. Thisbookisrecommendedforuseassupplementarymaterialbothinsideandoutside classroomsorasaself-learningguideforstudents,scientists,andresearcherswhodealwith numericdatainmolecularbiologyandrelated?elds. Thosewhostartasbeginners,but desiretobeatanintermediatelevel,will?ndthisbookespeciallyusefulintheirlearning pathway. WewanttothankJohnWalker(serieseditor),PatrickMarton,DavidCasey,andAnne Meagher,(editorsatSpringerandHumana)andShanthyJaganathan(Integra-India). The followingpersonsprovidedusefuladviceandcommentsonselectionoftopics,referralto expertsineachtopic,and/orchapterreviewsthatwetrulyappreciate:StephenLooney(a former editor of this book), Stan Young, Dmitri Zaykin, Douglas Hawkins, Wei Pan, Alexandre Almeida, John Ho, Rebecca Doerge, Paula Trushin, Kevin Morgan, Jason Osborne,PeterWestfall,JennyXiang,Ya-linChiu,YolandaBarron,HuiboShao,Alvin Mushlin,andRonaldFanta. Drs. Bang,Zhou,andMazumdarwerepartiallysupported byClinicalTranslationalScienceCenter(CTSC)grant(UL1-RR024996). HeejungBang vii Contents Preface...vii Contributors...xi PARTIBASICSTATISTICS...1 1. ExperimentalStatisticsforBiologicalSciences...3 HeejungBangandMarieDavidian 2. NonparametricMethodsforMolecularBiology...105 KnutM. WittkowskiandTingtingSong 3. BasicsofBayesianMethods...155 SujitK. Ghosh 4. TheBayesiant-TestandBeyond ...179 MithatGonen PARTII DESIGNSANDMETHODSFORMOLECULARBIOLOGY...201 5. SampleSizeandPowerCalculationforMolecularBiologyStudies...203 Sin-HoJung 6. DesignsforLinkageAnalysisandAssociationStudiesofComplexDiseases...219 YuehuaCui,GengxinLi,ShaoyuLi,andRonglingWu 7. IntroductiontoEpigenomicsandEpigenome-WideAnalysis...243 MelissaJ. FazzariandJohnM. Greally 8. Exploration,Visualization,andPreprocessingofHigh-DimensionalData...267 ZhijinWuandZhiqiangWu PARTIII STATISTICALMETHODSFORMICROARRAYDATA ...285 9. IntroductiontotheStatisticalAnalysisofTwo-ColorMicroarrayData...287 MartinaBremer,EdwardHimelblau,andAndreasMadlung 10. BuildingNetworkswithMicroarrayData...315 BradleyM. Broom,WareeRinsurongkawong,LajosPusztai, andKim-AnhDo PARTIV ADVANCEDORSPECIALIZEDMETHODSFORMOLECULARBIOLOGY. . 345 11. SupportVectorMachinesforClassi?cation:AStatisticalPortrait...347 YoonkyungLee 12. AnOverviewofClusteringAppliedtoMolecularBiology ...369 RebeccaNugentandMarinaMeila ix xContents 13. HiddenMarkovModelandItsApplicationsinMotifFindings...405 JingWuandJunXie 14. DimensionReductionforHigh-DimensionalData...417 LexinLi 15. IntroductiontotheDevelopmentandValidationofPredictiveBiomarker ModelsfromHigh-ThroughputDataSets ...435 XutaoDengandFabienCampagne 16. Multi-geneExpression-basedStatisticalApproachestoPredicting Patients'ClinicalOutcomesandResponses...471 FengCheng,Sang-HoonCho,andJaeK. Lee 17. Two-StageTestingStrategiesforGenome-WideAssociationStudies inFamily-BasedDesigns ...485 AmyMurphy,ScottT. Weiss,andChristophLange 18. StatisticalMethodsforProteomics ...497 KlausJung PARTVMETA-ANALYSISFORHIGH-DIMENSIONALDATA ...509 19. StatisticalMethodsforIntegratingMultipleTypesofHigh-ThroughputData. . 511 YangXieandChulAhn 20. ABayesianHierarchicalModelforHigh-DimensionalMeta-analysis...531 FeiLiu 21. MethodsforCombiningMultipleGenome-WideLinkageStudies...541 TreciaA. KippolaandStephanieA. Santorico PARTVI OTHERPRACTICALINFORMATION ...561 22. ImprovedReportingofStatisticalDesignandAnalysis:Guidelines, Education,andEditorialPolicies...5 63 MadhuMazumdar,SampritBanerjee,andHeatherL. VanEpps 23. StataCompanion...599 JenniferSousaBrennan SubjectIndex...627 Contributors CHULAHN* Division of Biostatistics, Department of Clinical Sciences, The Harold C.

The problem of probability interpretation was long overlooked before exploding in the 20th century, when the frequentist and subjectivist schools formalized two conflicting conceptions of probability. Beyond the radical followers of the two schools, a circle of pluralist thinkers tends to reconcile the opposing concepts. The author uses two theorems in order to prove that the various interpretations of probability do come into opposition and can be used in different contexts. The goal here is to clarify the multi fold nature of probability by means of a purely mathematical approach and to show how philosophical arguments can only serve to deepen actual intellectual contrasts. The book can be considered as one of the most important contributions in the analysis of probability interpretation in the last 10-15 years.

This volume celebrates the tenth edition of the Brazilian School of Probability (EBP), held at IMPA, Rio de Janeiro, from July 30 to August 4, 2006, jointly with the 69th Annual Meeting of the Institute of Mathematical Statistics. It was indeed an exceptional occasion for the local community working in this ?eld. The EBP, ?rst envisioned and organized in 1997, has since developed into an annual meeting with two or three advanced mini-courses and a high level conference. This volume grew up from invited or contributed articles by researchers that during the last ten yearshave been participating in the BrazilianSchool of Pro- bility. As a consequence, its content partially re?ects the topics that have pred- inated in the activities during the various editions of the School, with a strong - peal that comes from statistical mechanics and areasof concentrationthat include interacting particlesystems, percolation, random media anddisordered systems. All articles of this volume were peer-refereed.