Sandsynlighedsregning og statistik

This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner's overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Turan numbers and communication channels, etc.

Dieses Lehrbuch befasst sich leicht verständlich mit der Theorie der Kalman-Filterung. Die Autoren geben damit eine Einführung in Kalman-Filter und deren Anwendung für eingebettete Systeme. Zusätzlich wird anhand konkreter Praxisbeispiele der Kalman-Filterentwurf demonstriert ¿ Teilschritte werden im Buch ausführlich erläutert.Kalman-Filter sind die erste Wahl, um Störsignale auf den Sensorsignalen zu eliminieren. Dies ist von besonderer Bedeutung, da viele technische Systeme ihre prozessrelevanten Informationen über Sensoren gewinnen. Jeder Messwert eines Sensors weißt jedoch aufgrund verschiedener Ursachen einen Messfehler auf. Würde ein System nur auf Basis dieser ungenauen Sensorinformationen arbeiten, so wären viele Anwendungen, wie zum Beispiel ein Navigationssystem oder autonome arbeitende Systeme, nicht möglich.Das Buch ist geeignet für interessierte Bachelor- und Master-Studierende der Fachrichtungen Informatik, Maschinenbau, Elektrotechnik undMechatronik. Ebenso ist das Buch eine Hilfe für Ingenieure und Wissenschaftler, die ein Kalman-Filter z. B. für die Datenfusion oder die Schätzung unbekannter Größen in Echtzeitanwendungen einsetzen möchten.

"This concise book for scientists and students interested in bioinformatics and data science covers all aspects of predictive modeling for biomarker discovery based on high-dimensional data, as well as modern data science methods for identification of parsimonious and robust multivariate biomarkers for medical diagnosis and personalized medicine"--

IBM (international business machines) has published in its SPSS statistical software 2022 update a very important novel regression method entitled Kernel Ridge Regression (KRR). It is an extension of the currently available regression methods, and is suitable for pattern recognition in high dimensional data, particularly, when alternative methods fail. Its theoretical advantages are plenty and include thekernel trick for reduced arithmetic complexity,estimation of uncertainty by Gaussians unlike histograms,corrected data-overfit by ridge regularization,availability of 8 alternative kernel density models for datafit.A very exciting and wide array of preliminary KRR research has already been published by major disciplines (like studies in quantum mechanics and nuclear physics, studies of molecular affinity / dynamics, atomisation energy studies, but also forecasting economics studies, IoT (internet of things) studies for e-networks, plant stress response studies, big data streaming studies, etc). In contrast, it is virtually unused in clinical research. This edition is the first textbook and tutorial of kernel ridge regressions for medical and healthcare students as well as recollection / update bench, and help desk for professionals. Each chapter can be studied as a standalone, and, using, real as well as hypothesized data, it tests the performance of the novel methodology against traditional regression analyses. Step by step analyses of over 20 data files stored at Supplementary Files at Springer Interlink are included for self-assessment. We should add that the authors are well qualified in their field. Professor Zwinderman is past-president of the International Society of Biostatistics (2012-2015) and Professor Cleophas is past-president of the American College of Angiology (2000-2002). From their expertise they should be able to make adequate selections of modern KRR methods for the benefit of physicians, students, and investigators. The authors have been working and publishing together for 24 years and their research can be characterized as a continued effort to demonstrate that clinical data analysis is not mathematics but rather a discipline at the interface of biology and mathematics.

This book develops survey data analysis tools in Python, to create and analyze cross-tab tables and data visuals, weight data, perform hypothesis tests, and handle special survey questions such as Check-all-that-Apply. In addition, the basics of Bayesian data analysis and its Python implementation are presented. Since surveys are widely used as the primary method to collect data, and ultimately information, on attitudes, interests, and opinions of customers and constituents, these tools are vital for private or public sector policy decisions.As a compact volume, this book uses case studies to illustrate methods of analysis essential for those who work with survey data in either sector. It focuses on two overarching objectives:Demonstrate how to extract actionable, insightful, and useful information from survey data; andIntroduce Python and Pandas for analyzing survey data.

This book offers the reader a journey through the counterintuitive nature of Brownian motion under confinement. Diffusion is a universal phenomenon that controls a wide range of physical, chemical, and biological processes. The transport of spatially-constrained molecules and small particles is ubiquitous in nature and technology and plays an essential role in different processes. Understanding the physics of diffusion under conditions of confinement is essential for a number of biological phenomena and potential technological applications in micro- and nanofluidics, among others. Studies on diffusion under confinement are typically difficult to understand for young scientists and students because of the extensive background on diffusion processes, physics, and mathematics that is required. All of this information is provided in this book, which is essentially self-contained as a result of the authors¿ efforts to make it accessible to an audience of students from avariety of different backgrounds. The book also provides the necessary mathematical details so students can follow the technical process required to solve each problem. Readers will also find detailed explanations of the main results based on the last 30 years of research devoted to studying diffusion under confinement. The authors approach the physical problem from various angles and discuss the role of geometries and boundary conditions in diffusion. This textbook serves as a comprehensive and modern overview of Brownian motion under confinement and is intended for young scientists, graduate students, and advanced undergraduates in physics, physical chemistry, biology, chemistry, chemical engineering, biochemistry, bioengineering, and polymer and material sciences.

This report examines the effects that changes in laws-meant to encourage turnout and protect public health during the coronavirus disease 2019 (COVID-19) pandemic-had on voter turnout and the effects of in-person voting on the spread of COVID-19.

Life is full of uncertainty, risk, opportunity, and randomness. How can we gain an edge in our decision-making?There is much that we can neither predict nor control-but we can significantly improve our odds of favorable outcomes in both work and life. By developing an intuitive understanding of risk, chance, and uncertainty, we can harness the power of the randomness all around us to positively impact our lives.After two decades of investigation, Hossein Pishro-Nik distills his personal experience, research, and feedback from students into actionable methods that will help you make more confident decisions . . . even if you've never picked up a statistics book. You'll learn:Usable Insights: Practical applications of probability, statistics, finance, information theory, and machine learningEntrepreneurial Edge: Strategies to assess risk and make smarter business decisionsThe Unexpected Link: The surprising connection between privacy and randomnessAI in the Real World: Ways to apply lessons from the world of AI to our everyday decision-makingDemystifying the Complex: Accessible explanations of powerful mathematical concepts that, until now, have not been adequately covered for all readersPractical Uncertainty is a friendly, educational manual that uses real-world insights to help you internalize essential tools for risk-taking and decision-making in unpredictable scenarios. With this coherent and approachable book, you'll gain the knowledge and intuition to master the uncertainty in your life, improve your daily habits, and increase your chances of achieving your goals.

Stochastic elasticity is a fast developing field that combines nonlinear elasticity and stochastic theories in order to significantly improve model predictions by accounting for uncertainties in the mechanical responses of materials. However, in contrast to the tremendous development of computational methods for large-scale problems, which have been proposed and implemented extensively in recent years, at the fundamental level, there is very little understanding of the uncertainties in the behaviour of elastic materials under large strains.Based on the idea that every large-scale problem starts as a small-scale data problem, this book combines fundamental aspects of finite (large-strain) elasticity and probability theories, which are prerequisites for the quantification of uncertainties in the elastic responses of soft materials. The problems treated in this book are drawn from the analytical continuum mechanics literature and incorporate random variables as basic concepts along with mechanical stresses and strains. Such problems are interesting in their own right but they are also meant to inspire further thinking about how stochastic extensions can be formulated before they can be applied to more complex physical systems.

This book presents a comprehensive study covering the design and application of models and algorithms for assessing the joint device failures of telecommunication backbone networks caused by large-scale regional disasters. At first, failure models are developed to make use of the best data available; in turn, a set of fast algorithms for determining the resulting failure lists are described; further, a theoretical analysis of the complexity of the algorithms and the properties of the failure lists is presented, and relevant practical case studies are investigated. Merging concepts and tools from complexity theory, combinatorial and computational geometry, and probability theory, a comprehensive set of models is developed for translating the disaster hazard in informative yet concise data structures. The information available on the network topology and the disaster hazard is then used to calculate the possible (probabilistic) network failures. The resulting sets of resources that are expected to break down simultaneously are modeled as a collection of Shared Risk Link Groups (SRLGs), or Probabilistic SRLGs. Overall, this book presents improved theoretical methods that can help predicting disaster-caused network malfunctions, identifying vulnerable regions, and assessing precisely the availability of internet services, among other applications.