Sandsynlighedsregning og statistik

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space¿a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees.While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

This book deals with the first discriminant theory of linearly separable data (LSD), Theory3, based on the four ordinary LSD of Theory1 and 169 microarrays (LSD) of Theory2. Furthermore, you can quickly analyze the medical data with the misclassified patients which is the true purpose of diagnoses. Author developed RIP (Optimal-linear discriminant function finding the combinatorial optimal solution) as Theory1 in decades ago, that found the minimum misclassifications. RIP discriminated 63 (=26¿1) models of Swiss banknote (200*6) and found the minimum LSD: basic gene set (BGS). In Theory2, RIP discriminated Shipp microarray (77*7129) which was LSD and had only 32 nonzero coefficients (first Small Matryoshka; SM1). Because RIP discriminated another 7,097 genes and found SM2, the author developed the Matryoshka feature selection Method 2 (Program 3), that splits microarray into many SMs. Program4 can split microarray into many BGSs. Then, the wide columnLSD (Revolution-0), such as microarray (n5) models, including BGS, become LSD among (219¿1) models. Because Program2 confirms BGS has the minimum average error rate, BGS is the most compact and best model satisfying Occam¿s Razor. With this book, physicians obtain complete diagnostic results for disease, and engineers can become a true data scientist, by obtaining integral knowledge ofstatistics and mathematical programming with simple programs.

Dieses Lehrbuch betrachtet Data Management als interdisziplinäres Konzept mit Fokus auf den Zielen datengetriebener Unternehmen. Im Zentrum steht die interaktive Entwicklung eines Unternehmensdatenmodells für ein virtuelles Unternehmen mit Unterstützung eines online Learning Games unter Einbeziehung der Aufgaben, Ziele und Grundsätze des Data Managements, typischer Data-Management-Komponenten und Frameworks wie Datenmodellierung und Design, Metadaten Management, Data Architecture, und Data Governance, und verknüpft diese mit datengetriebenen Anwendungen wie Business Warehousing, Big Data, In-Memory Data Management, und Machine Learning im Data Management Kontext.Das Buch dient als Lehrbuch für Studierende der Informatik, der Wirtschaft und der Wirtschaftsinformatik an Universitäten, Hochschulen und Fachschulen und zur industriellen Aus- und Weiterbildung.

This book presents a variety of advanced statistical methods at a level suitable for advanced undergraduate and graduate students as well as for others interested in familiarizing themselves with these important subjects. It proceeds to illustrate these methods in the context of real-life applications in a variety of areas such as genetics, medicine, and environmental problems.The book begins in Part I by outlining various data types and by indicating how these are normally represented graphically and subsequently analyzed. In Part II, the basic tools in probability and statistics are introduced with special reference to symbolic data analysis. The most useful and relevant results pertinent to this book are retained. In Part III, the focus is on the tools of machine learning whereas in Part IV the computational aspects of BIG DATA are presented.This book would serve as a handy desk reference for statistical methods at the undergraduate and graduate level as well as be useful in courses which aim to provide an overview of modern statistics and its applications.

The volume includes a collection of peer-reviewed contributions from among those presented at the FNE, the main conference organized every two years by the Mexican Statistical Society (AME), and the 2020 AME Virtual Meeting. Statistical research in Latin America is prolific and research networks span both within and outside the region. As much of the work is typically carried out and published in Spanish, a large portion of the interested public is denied access to interesting findings, and the goal of this volume is therefore to provide access to selected works from Mexican collaborators and their international research networks to a wider audience. It may be especially attractive to academics interested in the latest methodological advances, while professionals from other disciplines may also find value in these new tools for data analysis. In 2021, the conference broadly focused on the interdisciplinary aspects of Statistics.

This book primarily aims to discuss emerging topics in statistical methods and to booster research, education, and training to advance statistical modeling on interval-censored survival data. Commonly collected from public health and biomedical research, among other sources, interval-censored survival data can easily be mistaken for typical right-censored survival data, which can result in erroneous statistical inference due to the complexity of this type of data. The book invites a group of internationally leading researchers to systematically discuss and explore the historical development of the associated methods and their computational implementations, as well as emerging topics related to interval-censored data. It covers a variety of topics, including univariate interval-censored data, multivariate interval-censored data, clustered interval-censored data, competing risk interval-censored data, data with interval-censored covariates, interval-censored data from electric medical records, and misclassified interval-censored data. Researchers, students, and practitioners can directly make use of the state-of-the-art methods covered in the book to tackle their problems in research, education, training and consultation.

This book discusses the role of mobile network data in urban informatics, particularly how mobile network data is utilized in the mobility context, where approaches, models, and systems are developed for understanding travel behavior. The objectives of this book are thus to evaluate the extent to which mobile network data reflects travel behavior and to develop guidelines on how to best use such data to understand and model travel behavior. To achieve these objectives, the book attempts to evaluate the strengths and weaknesses of this data source for urban informatics and its applicability to the development and implementation of travel behavior models through a series of the authors' research studies.Traditionally, survey-based information is used as an input for travel demand models that predict future travel behavior and transportation needs. A survey-based approach is however costly and time-consuming, and hence its information can be dated and limited to a particular region. Mobile network data thus emerges as a promising alternative data source that is massive in both cross-sectional and longitudinal perspectives, and one that provides both broader geographic coverage of travelers and longer-term travel behavior observation. The two most common types of travel demand model that have played an essential role in managing and planning for transportation systems are four-step models and activity-based models. The book's chapters are structured on the basis of these travel demand models in order to provide researchers and practitioners with an understanding of urban informatics and the important role that mobile network data plays in advancing the state of the art from the perspectives of travel behavior research.

This book is about data analytics, including problem definition, data preparation, and data analysis. A variety of techniques (e.g., regression, logistic regression, cluster analysis, neural nets, decision trees, and others) are covered with conceptual background as well as demonstrations of KNIME using each tool.The book uses KNIME, which is a comprehensive, open-source software tool for analytics that does not require coding but instead uses an intuitive drag-and-drop workflow to create a network of connected nodes on an interactive canvas. KNIME workflows provide graphic representations of each step taken in analyses, making the analyses self-documenting. The graphical documentation makes it easy to reproduce analyses, as well as to communicate methods and results to others. Integration with R is also available in KNIME, and several examples using R nodes in a KNIME workflow are demonstrated for special functions and tools not explicitly included in KNIME.

The book summarizes research work on the Wajid Sandstone, which provides integrated field and laboratory data to enable a detailed description of this unit including a facies analysis, porosity data, as well as permeability data to establish aquifer models. Detailed facies analysis at outcrop scale are supported by vertical and lateral sedimentological sections, facies and environmental analysis and supplemented by detailed laboratory petrographical and petrophysical data. The analysis and interpretation of the outcrop analog models include the reconstruction of the stratigraphic architecture at outcrop scale. Moreover, the results were described statistically, analyzed and eventually establish an outcrop-based aquifer model analogue. The book benefits undergraduate, graduate and researchers working on applied sedimentological studies, hydrogeology, statistical and geostatistical analysis and modeling.

This volume presents a collection of twenty-five peer-reviewed articles carefully selected from the contributions presented at the XXV Congress of the Portuguese Statistical Society (2021). Containing state-of-the-art developments in theoretical and applied statistics, the book will be accessible to readers with a background in mathematics and statistics, but will also be of interest to researchers from other scientific disciplines (e.g., biology, economics, medicine), who will find a broad range of relevant applications.

This book presents a selection of peer-reviewed contributions to the fifth Bayesian Young Statisticians Meeting, BaYSM 2021, held virtually due to the COVID-19 pandemic on 1-3 September 2021. Despite all the challenges of an online conference, the meeting provided a valuable opportunity for early career researchers, including MSc students, PhD students, and postdocs to connect with the broader Bayesian community.The proceedings highlight many different topics in Bayesian statistics, presenting promising methodological approaches to address important challenges in a variety of applications. The book is intended for a broad audience of people interested in statistics, and provides a series of stimulating contributions on theoretical, methodological, and computational aspects of Bayesian statistics.

This edited collection commemorates the career of Dr. S. Lynne Stokes by highlighting recent advances in her areas of research interest, emphasizing practical applications and future directions. It serves as a collective effort of leading statistical scientists who work at the cutting edge in statistical sampling.S. Lynne Stokes is Professor of Statistical Science and Director of the Data Science Institute at Southern Methodist University, and Senior Fellow at the National Institute of Statistical Sciences. She has enjoyed a distinguished research career, making fundamental contributions to a variety of fields in statistical sampling. Reflecting on Professor Stokes' main areas of research, this volume is structured into three main parts:I. ranked-set sampling, judgment post-stratified sampling, and capture-recapture methods II. nonsampling errors in statistical sampling III. educational and behavioral statistics.This collection will be of interest to researchers, advanced students, and professionals in the public and private sectors who would like to learn more about latest advancements in statistical sampling, particularly those who work in educational and behavioral statistics.

This book provides an overview of the emerging topics in biostatistical theories and methods through their applications to evidence-based global health research and decision-making. It brings together some of the top scholars engaged in biostatistical method development on global health to highlight and describe recent advances in evidence-based global health applications. The volume is composed of five main parts: data harmonization and analysis; systematic review and statistical meta-analysis; spatial-temporal modeling and disease mapping; Bayesian statistical modeling; and statistical methods for longitudinal data or survival data. It is designed to be illuminating and valuable to both expert biostatisticians and to health researchers engaged in methodological applications in evidence-based global health research. It is particularly relevant to countries where global health research is being rigorously conducted.

This book discusses state-of-the-art stochastic optimization algorithms for distributed machine learning and analyzes their convergence speed. The book first introduces stochastic gradient descent (SGD) and its distributed version, synchronous SGD, where the task of computing gradients is divided across several worker nodes. The author discusses several algorithms that improve the scalability and communication efficiency of synchronous SGD, such as asynchronous SGD, local-update SGD, quantized and sparsified SGD, and decentralized SGD. For each of these algorithms, the book analyzes its error versus iterations convergence, and the runtime spent per iteration. The author shows that each of these strategies to reduce communication or synchronization delays encounters a fundamental trade-off between error and runtime.

Arbeitsbuch Stochastik (Einführung und Grundzüge der Maßtheorie)Dieses Arbeitsbuch enthält die Aufgaben, Hinweise, Lösungen und Lösungswege der Kapitel 2 bis 8 des Lehrbuchs Stochastik: Eine Einführung mit Grundzügen der Maßtheorie. Durch die Offenlegung der Lösungswege und der Lösungen ist das Werk bestens geeignet zum Selbststudium, zur Vorlesungsbegleitung und als Prüfungsvorbereitung.Das Werk umfasst mehr als 330 Übungsaufgaben, die in Verständnisfragen, Beweisaufgaben und Rechenaufgaben gegliedert sind, und ist in der vorliegenden zweiten Auflage auf die zweite Auflage des Hauptwerks angepasst.

This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind. The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions. Presents definitions and theorems that highlight key concepts and worked examples to illustrate the various applicationsContains numerous exercises at varying levels of difficulty that consolidate the presented concepts and resultsIncludes hints and answers to all exercises via the appendix and is supplemented with an Instructor's Solution Manual

These proceedings address the latest developments in the broad area of intelligent construction integrated in the mission of the International Society for Intelligent Construction (ISIC) which aims to promote intelligent construction technologies applications from the survey, design, construction, operation, and maintenance/rehabilitation by adapting to changes of environments and minimizing risks. Its goals are to improve the quality of construction, cost-saving, and safety, exploring fundamental issues related to the application and use of Artificial Intelligence (AI) and Machine Learning techniques and technology.ISIC 2022 is the 3rd ISIC international conference, held in Guimares, Portugal on September 6-9, 2022, and follows the previous successful instalments of the conference series in China (2019) and USA (2017). It took a holistic approach to integrate civil engineering, construction machinery, electronic sensor technology, survey/testing technologies, information technology/computing, and other related fields in the broad area of intelligent construction. The respective contributions cover the following topics: Artificial Intelligence for Design and the Built Environment, Building Information Modelling (BIM) and Construction Automation and Robotics, Intelligent Construction, Sustainable Construction, and Sustainable and Smart Infrastructures.Given its broad range of coverage, the book will benefit students, educators, researchers and professionals practitioners alike, encouraging these readers to help the intelligent construction community into the digital era and with a vision on societal issues.

This book is designed as a textbook for graduate students and as a resource for researchers seeking a thorough mathematical treatment of its subject. It develops the main results of regression and the analysis of variance, as well as the central results on confounded and fractional factorial experiments. Matrix theory is deemphasized; its role is taken instead by the theory of linear transformations between vector spaces.The text gives a carefully paced and unified presentation of two topics, linear models and experimental design. Students are assumed to have a solid background in linear algebra, basic knowledge of regression and analysis of variance, and some exposure to experimental design, and should be comfortable with reading and constructing mathematical proofs.The book leads students into the mathematical theory, including many examples both for motivation and for illustration. Over 130 exercises of varying difficulty are included. An extensive mathematical appendix and a detailed index make the text especially accessible.Linear Models and Design can serve as a textbook for a year-long course in the topics covered, or for a one-semester course in either linear model theory or experimental design. It prepares students for more advanced topics in the field, and assists in developing a thoughtful approach to the existing literature. It includes a guide to terminology as well as discussion of the history and development of ideas, and offers a fresh perspective on the fundamental concepts and results of the subject.

The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure  of the integrator process, they generalize the usual Ito and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness.  It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.

This book discusses the interplay between statistics, data science, machine learning and artificial intelligence, with a focus on environmental science, the natural sciences, and technology. It covers the state of the art from both a theoretical and a practical viewpoint and describes how to successfully apply machine learning methods, demonstrating the benefits of statistics for modeling and analyzing high-dimensional and big data. The book's expert contributions include theoretical studies of machine learning methods, expositions of general methodologies for sound statistical analyses of data as well as novel approaches to modeling and analyzing data for specific problems and areas. In terms of applications, the contributions deal with data as arising in industrial quality control, autonomous driving, transportation and traffic, chip manufacturing, photovoltaics, football, transmission of infectious diseases, Covid-19 and public health. The book will appeal to statisticians and data scientists, as well as engineers and computer scientists working in related fields or applications.

Dieses Lehrbuch liefert einen verständnisorientierten Einstieg in die asymptotische Stochastik. Es ist vom Niveau her zu Beginn eines Mathematik-Masterstudiums angesiedelt und deckt den Stoff ab, der in einer vierstündigen Vorlesung mit zweistündigen Übungen vermittelt werden kann. Einzelne Kapitel eignen sich zudem für Seminare am Ende eines Bachelorstudiums.Neben eher grundständigen Themen wie der Momentenmethode zum Nachweis von Verteilungskonvergenz oder dem multivariaten zentralen Grenzwertsatz und der Delta-Methode werden unter anderem Grenzwertsätze für U-Statistiken und der Satz von Donsker sowie die Brown'sche Brücke mit Anwendungen auf die Statistik behandelt. Das Buch schließt mit einem zentralen Grenzwertsatz für hilbertraumwertige Zufallselemente mit Anwendungen auf gewichtete L²-Statistiken.Ein besonderes Merkmal des Buches sind mehr als 130 Selbstfragen, die am Ende des jeweiligen Kapitels beantwortet werden, sowie mehr als 180 Übungsaufgaben mit Lösungen. Hierdurch eignet sich dieses Werk sehr gut zum Selbststudium.Die 2. Auflage ist vollständig durchgesehen und thematisch unter anderem um die starke Konsistenz der Maximum-Likelihood-Schätzung sowie zentrale Grenzwertsätze für Dreiecksschemata von Zufallsvektoren und hilbertraumwertigen Zufallsvariablen erweitert. Hinzugekommen sind auch weitere Beispiele sowie 11 neue Aufgaben mit Lösungen.

This book, fully updated for Python version 3.6+, covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules in these areas.  All the figures and numerical results are reproducible using the Python codes provided. The author develops key intuitions in machine learning by working meaningful examples using multiple analytical methods and Python codes, thereby connecting theoretical concepts to concrete implementations. Detailed proofs for certain important results are also provided. Modern Python modules like Pandas, Sympy, Scikit-learn, Tensorflow, and Keras are applied to simulate and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, and regularization. Many abstract mathematical ideas, such as convergence in probability theory, are developed and illustrated with numerical examples. This updated edition now includes the Fisher Exact Test and the Mann-Whitney-Wilcoxon Test. A new section on survival analysis has been included as well as substantial development of Generalized Linear Models. The new deep learning section for image processing includes an in-depth discussion of gradient descent methods that underpin all deep learning algorithms.   As with the prior edition, there are new and updated *Programming Tips* that the illustrate effective Python modules and methods for scientific programming and machine learning. There are 445 run-able code blocks with corresponding outputs that have been tested for accuracy.  Over 158 graphical visualizations (almost all generated using Python) illustrate the concepts that are developed both in code and in mathematics. We also discuss and use key Python modules such as Numpy, Scikit-learn, Sympy,  Scipy, Lifelines, CvxPy, Theano, Matplotlib, Pandas, Tensorflow, Statsmodels,  and Keras.This book is suitable for anyone with an undergraduate-level exposure to probability, statistics, or machine learning and with rudimentary knowledge of Python programming.

This graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.The material provided should aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes.