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.

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.

Exploratory data analysis (EDA) is about detecting and describing patterns, trends, and relations in data, motivated by certain purposes of investigation. As something relevant is detected in data, new questions arise, causing specific parts to be viewed in more detail. So EDA has a significant appeal: it involves hypothesis generation rather than mere hypothesis testing.

The authors describe in detail and systemize approaches, techniques, and methods for exploring spatial and temporal data in particular. They start by developing a general view of data structures and characteristics and then build on top of this a general task typology, distinguishing between elementary and synoptic tasks. This typology is then applied to the description of existing approaches and technologies, resulting not just in recommendations for choosing methods but in a set of generic procedures for data exploration.

Professionals practicing analysis will profit from tested solutions a" illustrated in many examples a "for reuse in the catalogue of techniques presented. Students and researchers will appreciate the detailed description and classification of exploration techniques, which are not limited to spatial data only. In addition, the general principles and approaches described will be useful for designers of new methods for EDA.

This volume originates from the INDAM Symposium on Trends on Applications of Mathematics to Mechanics (STAMM), which was held at the INDAM headquarters in Rome on 5-9 September 2016. It brings together original contributions at the interface of Mathematics and Mechanics. The focus is on mathematical models of phenomena issued from various applications. These include thermomechanics of solids and gases, nematic shells, thin films, dry friction, delamination, damage, and phase-field dynamics. The papers in the volume present novel results and identify possible future developments. The book is addressed to researchers involved in Mathematics and its applications to Mechanics.

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 series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book s primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes. Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes: * Multiple examples from disciplines such as business, mathematical finance, and engineering * Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material * A rigorous treatment of all probability and stochastic processes concepts An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.

Signal detection theory, as developed in electrical engineering and based on statistical decision theory, was first applied to human sensory discrimination about 40 years ago. The theory's intent was to explain how humans discriminate and how we might use reliable measures to quantify this ability. An interesting finding of this work is that decisions are involved even in the simplest of discrimination tasks--say, determining whether or not a sound has been heard (a yes-no decision). Detection theory has been applied to a host of varied problems (for example, measuring the accuracy of diagnostic systems, survey research, reliability of lie detection tests) and extends far beyond the detection of signals. This book is a primer on signal detection theory, useful for both undergraduates and graduate students.

The book provides complete coverage of the classical methods of statistical analysis. It is designed to give students an understanding of the purpose of statistical analyses, to allow the student to determine, at least to some degree, the correct type of statistical analyses to be performed in a given situation, and have some appreciation of what constitutes good experimental design.
* Examples and exercises contain real data and
graphical illustration for ease of interpretation
* Outputs from SAS 7, SPSS 7, Excel, and Minitab are
used for illustration, but any major statistical
software package will work equally well.
* Data sets are furnished on CD included in the text

Rapid technological advances in devices used for data collection have led to the emergence of a new class of longitudinal data: intensive longitudinal data (ILD). Behavioral scientific studies now frequently utilize handheld computers, beepers, web interfaces, and other technological tools for collecting many more data points over time than previously possible. Other protocols, such as those used in fMRI and monitoring of public safety, also produce ILD, hence the statistical models in this volume are applicable to a range of data. The volume features state-of-the-art statistical modeling strategies developed by leading statisticians and methodologists working on ILD in conjunction with behavioral scientists. Chapters present applications from across the behavioral and health sciences, including coverage of substantive topics such as stress, smoking cessation, alcohol use, traffic patterns, educational performance and intimacy.
Models for Intensive Longitudinal Data (MILD) is designed for those who want to learn about advanced statistical models for intensive longitudinal data and for those with an interest in selecting and applying a given model. The chapters highlight issues of general concern in modeling these kinds of data, such as a focus on regulatory systems, issues of curve registration, variable frequency and spacing of measurements, complex multivariate patterns of change, and multiple independent series. The extraordinary breadth of coverage makes this an indispensable reference for principal investigators designing new studies that will introduce ILD, applied statisticians working on related models, and methodologists, graduate students, and applied analysts working in arange of fields. A companion Web site at www.oup.com/us/MILD contains program examples and documentation.

The state-of-the-art of multivariate analysis in sensory science is described in this volume. Both methods for aggregated and individual sensory profiles are discussed. Processes and results are presented in such a way that they can be understood not only by statisticians but also by experienced sensory panel leaders and users of sensory analysis.

The techniques presented are focused on examples and interpretation rather than on the technical aspects, with an emphasis on new and important methods which are possibly not so well known to scientists in the field. Important features of the book are discussions on the relationship among the methods with a strong accent on the connection between problems and methods. All procedures presented are described in relation to sensory data and not as completely general statistical techniques.

Sensory scientists, applied statisticians, chemometricians, those working in consumer science, food scientists and agronomers will find this book of value.

This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference.

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.

This book provides an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

This book is a useful overview of results in multivariate probability distributions and multivariate analysis as well as a reference to harmonic analysis on symmetric cones adapted to the needs of researchers in analysis and probability theory.

This is a practical guide to solutions for forecasting demand for services and products in international markets - and much more than just a listing of dry theoretical methods. Leading experts present studies on improving methods for forecasting numbers of incoming patent filings at the European Patent Office. These are reviewed by practitioners of the existing methods, revealing that it may not always be wise to trust established regression approaches.

This book provides a modern, hands-on guide to the essential concepts and ideas for analyzing data with missing observations in the field of biostatistics. It acknowledges the limitations of established techniques and provides concrete applications of newly developed methods. It covers traditional techniques for missing data inference including likelihood-based, weighted GEE, multiple imputation, and Bayesian methods and applies the methodology to rapidly developing areas of research. The book is ideal for courses on biostatistics at the upper-undergraduate and graduate levels and for health science researchers and applied statisticians.

This book presents the foundations of key problems in computational molecular biology and bioinformatics. It focuses on computational and statistical principles applied to genomes, and introduces the mathematics and statistics that are crucial for understanding these applications. The book features a free download of the R software statistics package and the text provides great crossover material that is interesting and accessible to students in biology, mathematics, statistics and computer science. More than 100 illustrations and diagrams reinforce concepts and present key results from the primary literature. Exercises are given at the end of chapters.

This volume presents a concise and practical overview of statistical methods and tables not readily available in other publications. It begins with a review of the commonly used continuous and discrete probability distributions. Several useful distributions that are not so common and less understood are described with examples and applications in full detail: discrete normal, left-partial, right-partial, left-truncated normal, right-truncated normal, lognormal, bivariate normal, and bivariate lognormal. Table values are provided with examples that enable researchers to easily apply the distributions to real applications and sample data. The left- and right-truncated normal distributions offer a wide variety of shapes in contrast to the symmetrically shaped normal distribution, and a newly developed spread ratio enables analysts to determine which of the three distributions best fits a particular set of sample data. The book will be highly useful to anyone who does statistical and probability analysis. This includes scientists, economists, management scientists, market researchers, engineers, mathematicians, and students in many disciplines.

Advances in Growth Curve Models: Topics from the Indian Statistical Institute is developed from the Indian Statistical Institute's A National Conference on Growth Curve Models. This conference took place between March 28-30, 2012 in Giridih, Jharkhand, India. Jharkhand is a tribal area. Advances in Growth Curve Models: Topics from the Indian Statistical Institute shares the work of researchers in growth models used in multiple fields. A growth curve is an empirical model of the evolution of a quantity over time. Case studies and theoretical findings, important applications in everything from health care to population projection, form the basis of this volume. Growth curves in longitudinal studies are widely used in many disciplines including: Biology, Population studies, Economics, Biological Sciences, SQC, Sociology, Nano-biotechnology, and Fluid mechanics. Some included reports are research topics that have just been developed, whereas others present advances in existing literature. Both included tools and techniques will assist students and researchers in their future work. Also included is a discussion of future applications of growth curve models.

The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. This book gives, for the first time in book form, a comprehensive and up-to-date account of this modern theory. Many major classes of designs are covered in the book. While maintaining a high level of mathematical rigor, it also provides extensive design tables for research and practical purposes. Apart from being useful to researchers and practitioners, the book can form the core of a graduate level course in experimental design.

The Minimum Message Length (MML) Principle is an information-theoretic approach to induction, hypothesis testing, model selection, and statistical inference. MML, which provides a formal specification for the implementation of Occam's Razor, asserts that the a ~besta (TM) explanation of observed data is the shortest. Further, an explanation is acceptable (i.e. the induction is justified) only if the explanation is shorter than the original data.

This book gives a sound introduction to the Minimum Message Length Principle and its applications, provides the theoretical arguments for the adoption of the principle, and shows the development of certain approximations that assist its practical application. MML appears also to provide both a normative and a descriptive basis for inductive reasoning generally, and scientific induction in particular. The book describes this basis and aims to show its relevance to the Philosophy of Science.

Statistical and Inductive Inference by Minimum Message Length will be of special interest to graduate students and researchers in Machine Learning and Data Mining, scientists and analysts in various disciplines wishing to make use of computer techniques for hypothesis discovery, statisticians and econometricians interested in the underlying theory of their discipline, and persons interested in the Philosophy of Science. The book could also be used in a graduate-level course in Machine Learning and Estimation and Model-selection, Econometrics and Data Mining.

"Any statistician interested in the foundations of the discipline, or the deeper philosophical issues of inference, will find this volume a rewarding read." Short Book Reviews of theInternational Statistical Institute, December 2005

My ?rst encounter with the world of crime and punishment was more than two decades ago, and it has since undergone vast changes. No one could have foreseen that crime-related problems would occupy such a prominent position in cultural awareness. Crime is on the rise, the public attention devoted to it has increased even more, and its political importance has mushroomed. The major change in the 1990s was perhaps the transformation of crime into a safety issue. Crime is no longer a matter involving offenders, victims, the police and the courts, it involves everyone and any number of agencies and institutions from security companies to the local authorities and from schools to pub and restaurant owners. Crime has become a much larger complex than the judicial system-a complex organized mentally and institutionally around this one concept of safety. In this book I make an effort to get to the bottom of this complex. It is the sequel to my dissertation Crime and Morality-The Moral Signi?cance of Criminal Justice in a Postmodern Culture (2000), where I hold that the victim became the essence of crime in Western culture, and that this in turn shaped public morality. In the second half of the twentieth century, a personal morality based on an awareness of our own and other people's vulnerability, i. e. potential victimhood, succeeded the ethics of duty.