Sandsynlighedsregning og statistik

This book is an easy-to-read reference providing a link between functional analysis and diffusion processes. More precisely, the book takes readers to a mathematical crossroads of functional analysis (macroscopic approach), partial differential equations (mesoscopic approach), and probability (microscopic approach) via the mathematics needed for the hard parts of diffusion processes. This work brings these three fields of analysis together and provides a profound stochastic insight (microscopic approach) into the study of elliptic boundary value problems.The author does a massive study of diffusion processes from a broad perspective and explains mathematical matters in a more easily readable way than one usually would find. The book is amply illustrated; 14 tables and 141 figures are provided with appropriate captions in such a fashion that readers can easily understand powerful techniques of functional analysis for the study of diffusion processes in probability.The scope of the author's work has been and continues to be powerful methods of functional analysis for future research of elliptic boundary value problems and Markov processes via semigroups. A broad spectrum of readers can appreciate easily and effectively the stochastic intuition that this book conveys.  Furthermore, the book will serve as a sound basis both for researchers and for graduate students in pure and applied mathematics who are interested in a modern version of the classical potential theory and Markov processes.For advanced undergraduates working in functional analysis, partial differential equations, and probability, it provides an effective opening to these three interrelated fields of analysis. Beginning graduate students and mathematicians in the field looking for a coherent overview will find the book to be a helpful beginning. This work will be a major influence in a very broad field of study for a long time.

This unique book addresses the bioinformatic and statistical modelling and also the analysis of microbiome data using cutting-edge QIIME 2 and R software. It covers core analysis topics in both bioinformatics and statistics, which provides a complete workflow for microbiome data analysis: from raw sequencing reads to community analysis and statistical hypothesis testing. It includes real-world data from the authors¿ research and from the public domain, and discusses the implementation of QIIME 2 and R for data analysis step-by-step. The data as well as QIIME 2 and R computer programs are publicly available, allowing readers to replicate the model development and data analysis presented in each chapter so that these new methods can be readily applied in their own research. Bioinformatic and Statistical Analysis of Microbiome Data is an ideal book for advanced graduate students and researchers in the clinical, biomedical, agricultural, and environmental fields, as well as those studying bioinformatics, statistics, and big data analysis.

Forecasting from multi-equation models has very rarely been the focus in econometric literature. In response, this book presents a range of methodologies to approach this complex field and offers readers essential information on forecasting from multi-equation econometric micromodels.In the twentieth century, significant interest in econometric macromodels emerged. These multi-equation models are mostly systems of interdependent equations, most often used to describe the national economies of various countries. The book analyzes econometric forecasting procedures and illustrates them with empirical examples that are based on real economic (mostly business-derived) data. The procedure of forecast building from systems of interdependent equations is presented for two categories of econometric models: models with a feedback effect and models with closed-loop links between interdependent variables. The forecasts obtained via this technique are compared with the results derived from reduced-form equations of the respective econometric model. The author also generalizes the rules of the reduced-recursive (helical, iterative) procedure application, against the backdrop of the proposed method of forecast building from reduced-form equations of systems of interdependent equations. Given its scope, the book will appeal not only to PhD students and researchers, but also undergraduate students and academics in general.

This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariants for directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.

This book provides an overview of statistical concepts and basic methodology for the study of genetics of human traits and diseases. It attempts to provide a step-by-step description of problem identification, study design, methodology of data collection, data exploration, data summarization and visualization, and more advanced analytical methods for inferring genetic underpinnings of human phenotypes. The book provides codes in R programming language for implementation of most of the statistical methods described, which will enable practitioners to perform analysis of data on their own, without having to mold the data to fit the requirements of commercial statistical packages. Useful to anyone engaged in studies to understand and manage good health, the book is a useful guide for sustainable development of humankind. Primarily intended for practicing biologists especially those who carry out quantitative biological research, in particular, human geneticists, the book is also helpful in classroom teaching.

This book discusses chemometric methods for spectroscopy analysis including NIR, MIR, Raman, NMR, and LIBS, from the perspective of practical applied spectroscopy. It covers all aspects of chemometrics associated with analytical spectroscopy, including representative sample selection algorithm, outlier detection algorithm, model updating and maintenance algorithm and strategy and calibration performance evaluation methods.To provide a systematic and comprehensive overview the latest progress of chemometric methods including recent scientific research and practical applications are presented. In addition the book also highlights the improvement of classical algorithms and the extension of common strategies. It is therefore useful as a reference book for researchers engaged in analytical spectroscopy technology, chemometrics, analytical instruments and other related fields.

This book explains concepts and techniques for business analytics and demonstrate them on real life applications for managers and practitioners. It illustrates how machine learning and optimization techniques can be used to implement intelligent business automation systems. The book examines business problems concerning supply chain, marketing & CRM, financial, manufacturing and human resources functions and supplies solutions in Python.

This text presents the basic theory of random walks on infinite, finitely generated groups, along with certain background material in measure-theoretic probability. The main objective is to show how structural features of a group, such as amenability/nonamenability, affect qualitative aspects of symmetric random walks on the group, such as transience/recurrence, speed, entropy, and existence or nonexistence of nonconstant, bounded harmonic functions. The book will be suitable as a textbook for beginning graduate-level courses or independent study by graduate students and advanced undergraduate students in mathematics with a solid grounding in measure theory and a basic familiarity with the elements of group theory. The first seven chapters could also be used as the basis for a short course covering the main results regarding transience/recurrence, decay of return probabilities, and speed. The book has been organized and written so as to be accessible not only to students in probability theory, but also to students whose primary interests are in geometry, ergodic theory, or geometric group theory.

Die Beiträge der Wissenschaft in der Corona-Krise waren vielfältig. Sie reichten von der Impfstoffentwicklung über Aerosolforschung bis hin zu Modellierungen. Es gab viele Erfolgsmeldungen. Virologen wurden zu Medienstars. Wissenschaft, Politik und Medien sprachen zeitweise mit einer Stimme ¿ ein Siegeszug der Wissenschaftskommunikation? Es gab aber auch überzogene Versprechungen, dünnhäutige Reaktionen bei Kritik und Einseitigkeit in der Politikberatung ¿ ein kommunikatives Desaster für Wissenschaft, Politik und Medien?Dieses Sachbuch möchte die Diskussion zur Corona-Kommunikation in Wissenschaft, Politik und Medien anregen. Es basiert auf Fallstudien, die aus verschiedenen Perspektiven beleuchtet werden, ordnet Beispiele entlang der Kriterien etablierter Wissenschaftsorganisationen ein und formuliert Fragen an die künftige Wissenschaft und ihre Kommunikation.Ist dies eine Studie, Materialsammlung oder Streitschrift? Alles. Aber hauptsächlich ein Plädoyer: Gegen unantastbare Wahrheiten, Meinungshomogenisierung und Ausgrenzung. Für Transparenz, Pluralität und Dialog in Wissenschaft und Kommunikation.

This book offers an introduction to applied statistics through data analysis, integrating statistical computing methods. It covers robust and non-robust descriptive statistics used in each of four bivariate statistical models that are commonly used in research: ANOVA, proportions, regression, and logistic. The text teaches statistical inference principles using resampling methods (such as randomization and bootstrapping), covering methods for hypothesis testing and parameter estimation. These methods are applied to each statistical model introduced in preceding chapters.Data analytic examples are used to teach statistical concepts throughout, and students are introduced to the R packages and functions required for basic data analysis in each of the four models. The text also includes introductory guidance to the fundamentals of data wrangling, as well as examples of write-ups so that students can learn how to communicate findings. Each chapter includes problems forpractice or assessment. Supplemental instructional videos are also available as an additional aid to instructors, or as a general resource to students. This book is intended for an introductory or basic statistics course with an applied focus, or an introductory analytics course, at the undergraduate level in a two-year or four-year institution. This can be used for students with a variety of disciplinary backgrounds, from business, to the social sciences, to medicine. No sophisticated mathematical background is required.

This textbook presents the basics of probability and statistical estimation, with a view to applications. The didactic presentation follows a path of increasing complexity with a constant concern for pedagogy, from the most classical formulas of probability theory to the asymptotics of independent random sequences and an introduction to inferential statistics. The necessary basics on measure theory are included to ensure the book is self-contained. Illustrations are provided from many applied fields, including information theory and reliability theory. Numerous examples and exercises in each chapter, all with solutions, add to the main content of the book.Written in an accessible yet rigorous style, the book is addressed to advanced undergraduate students in mathematics and graduate students in applied mathematics and statistics. It will also appeal to students and researchers in other disciplines, including computer science, engineering, biology, physics and economics, who are interested in a pragmatic introduction to the probability modeling of random phenomena.

This book focuses on the Frobenius theorem regarding a nonlinear simultaneous system. The Frobenius theorem is well known as a condition for a linear simultaneous system¿s having a nonnegative solution. Generally, however, the condition of a simultaneous system, including a non-linear system¿s having a nonnegative solution, is hardly discussed at all. This book, therefore, extends the conventional Frobenius theorem for nonlinear simultaneous systems for economic analysis. Almost all static optimization problems in economics involve nonlinear programing. Theoretical models in economics are described in the form of a simultaneous system resulting from the rational optimization behavior of households and enterprises. On the other hand, rational optimization behavior of households and enterprises is, mathematically speaking, expressed as nonlinear programing. For this reason it is important to understand the meaning of nonlinear programing. Because this book includes explanations of the relations among various restrictions in a nonlinear programing systematically and clearly, this book is suitable for students in graduate school programs in economics.

Baseball is not the only sport to use "moneyball." American football teams, fantasy football players, fans, and gamblers are increasingly using data to gain an edge on the competition. Professional and college teams use data to help identify team needs and select players to fill those needs. Fantasy football players and fans use data to try to defeat their friends, while sports bettors use data in an attempt to defeat the sportsbooks. In this concise book, Eric Eager and Richard Erickson provide a clear introduction to using statistical models to analyze football data using both Python and R. Whether your goal is to qualify for an entry-level football analyst position, dominate your fantasy football league, or simply learn R and Python with fun example cases, this book is your starting place. Through case studies in both Python and R, you'll learn to: Obtain NFL data from Python and R packages and web scraping Visualize and explore data Apply regression models to play-by-play data Extend regression models to classification problems in football Apply data science to sports betting with individual player props Understand player athletic attributes using multivariate statistics

This comprehensive open access book enables readers to discover the essential techniques for load forecasting in electricity networks, particularly for active distribution networks.From statistical methods to deep learning and probabilistic approaches, the book covers a wide range of techniques and includes real-world applications and a worked examples using actual electricity data (including an example implemented through shared code). Advanced topics for further research are also included, as well as a detailed appendix on where to find data and additional reading. As the smart grid and low carbon economy continue to evolve, the proper development of forecasting methods is vital. This book is a must-read for students, industry professionals, and anyone interested in forecasting for smart control applications, demand-side response, energy markets, and renewable utilization.

This text describes a comprehensive adjoint sensitivity analysis methodology (nth-CASAM), developed by the author, which enablesthe efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The nth-CASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby overcoming the so-called ¿curse of dimensionality¿ in sensitivity and uncertainty analysis. The nth-CASAM is applicable to any model; the larger the number of model parameters, the more efficient the nth-CASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling.This Volume Two, the second of three, presents the large-scale application of the nth-CASAM to perform a representative fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark is modeled mathematically by the Boltzmann particle transport equation, involving 21,976 imprecisely-known parameters, the numerical solution of which requires representative large-scale computations. The sensitivity analysis presented in this volume is the most comprehensive ever performed in the field of reactor physics and the results presented in this book prove, perhaps counter-intuitively, that many of the 4th-order sensitivities are much larger than the corresponding 3rd-order ones, which are, in turn, much larger than the 2nd-order ones, all of which are much larger than the 1st-order sensitivities. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of exactly obtained expressions of arbitrarily-high-order response sensitivities.

This book is designed to provide a comprehensive introduction to R programming for data analysis, manipulation and presentation. It covers fundamental data structures such as vectors, matrices, arrays and lists, along with techniques for exploratory data analysis, data transformation and manipulation. The book explains basic statistical concepts and demonstrates their implementation using R, including descriptive statistics, graphical representation of data, probability, popular probability distributions and hypothesis testing. It also explores linear and non-linear modeling, model selection and diagnostic tools in R.The book also covers flow control and conditional calculations by using ¿¿if¿¿ conditions and loops and discusses useful functions and resources for further learning. It provides an extensive list of functions grouped according to statistics classification, which can be helpful for both statisticians and R programmers. The use of different graphic devices, high-level and low-level graphical functions and adjustment of parameters are also explained. Throughout the book, R commands, functions and objects are printed in a different font for easy identification. Common errors, warnings and mistakes in R are also discussed and classified with explanations on how to prevent them.

This book introduces an integrated conceptual framework of the China Seismic Experimental Site (CSES), describes its scientific challenges and research priorities, and reports preliminary results coming out of observational infrastructure in seismology, tectonophysics, geodesy, geophysics and geochemistry. Preliminary community fault model, community velocity model, and community strain rate model in the CSES are described in this book. A multidisciplinary test observation system includes GNSS, seismic array, and deep drilling system under construct around middle segment of the Xiansuihe-Xiaojiang fault and other seismogenic faults in the CSES which are also introduced. This book introduces multidisciplinary topics and a wide spectrum of solid earth system to describe various disciplines, methods, and techniques through the CSES. This book presents a vision of the CSES that is dedicated to deepen the scientific understanding of continental earthquake preparation and occurrence and enhance the disaster resilience of the society. It aims at establishing a field laboratory of earthquake science, in which international and interdisciplinary cooperation could be fostered and supported. Contents of this book include the following:* History of Seismic Experiment Sites in the World.* Launching of CSES Project: Seismicity, Existed Earthquake Monitoring Networks, and Historical Seismic Disasters.* Seismotectonics and Geodynamics of the Eastern Margin of the Tibetan Plateau with Implication for the CSES.* Theoretical Framework of CSES in View of Natural Science and in view of Social Science.*  Updated Earthquake Monitoring Network in China.*  CSES Community Models of Geology, Structure, and Deformation.*  Earthquake Forecasting Models.*  CSES Products: Massive Data Procession and Distribution.*  A Review of the Field Expedition of the June 17, 2019, Changning, Sichuan, M6.0 Earthquake.*  Rupture Structure and Earthquake Risk of the South Longmenshan Fault Viewed by Guided Waves.*  Seismic Risk Assessment.*  Model of a Seismic Experimental Site with Application to the Comparative Study between CSES and ASES.  

Probability is tough - even those fairly well versed in statistical analysis balk at the prospect of tackling it. Many probability concepts seem counterintuitive at first, and the successful student must in effect train him or herself to think in a totally new way. Mastery of probability takes a lot of time, and only comes from solving many, many problems.The aim of this text and its companion, The Probability Workbook (coming soon), is to present the subject of probability as a tutor would. Probability concepts are explained in everyday language and worked examples are presented in abundance. In addition to paper-and-pencil solutions, solution strategies using Microsoft Excel functions are given. All mathematical symbols are explained, and the mathematical rigor is kept on an algebra level; calculus is avoided.This book is written for quality practitioners who are currently performing statistical and probability analyses in their workplaces, and for those seeking to learn probability concepts for the American Society for Quality (ASQ) Certified Quality Engineer, Reliability Engineer, Six Sigma Green Belt, Black Belt, or Master Black Belt exams.

This book describes how reliability can be embedded into the product development using a design methodology that uses parametric accelerated lifecycle testing (ALT) .The book has these features:¿ A new reliability methodology, based on inferential statistics, that can determine whether the reliability of a mechanical/civil system is achieved.¿ A unique reliability methodology to prevent reliability disasters in new mechanical products in the field, e.g., automobiles and airplanes.¿ Robust design methodology of mechanical/civil product to withstand a variety of loads.¿ Explanation of an alternative experimental Taguchi methodology.¿ Discussion of how parametric ALT can alsobe used to predict product reliability¿lifetime and failure rate.¿ Detailed case studies that demonstrate parametric ALT methodology.This book will be useful for senior-level undergraduate and graduate students, professional engineers, college and university-level lecturers, researchers, and design managers in mechanical and civil engineering.

This book provides a reference for people working in the design, development, and manufacturing of medical devices. ¿While there are no statistical methods specifically intended for medical devices, there are methods that are commonly applied to various problems in the design, manufacturing, and quality control of medical devices. The aim of this book is not to turn everyone working in the medical device industries into mathematical statisticians; rather, the goal is to provide some help in thinking statistically, and knowing where to go to answer some fundamental questions, such as justifying a method used to qualify/validate equipment, or what information is necessary to support the choice of sample sizes.While, there are no statistical methods specifically designed for analysis of medical device data, there are some methods that seem to appear regularly in relation to medical devices. For example, the assessment of receiver operating characteristic curves is fundamental to development of diagnostic tests, and accelerated life testing is often critical for assessing the shelf life of medical device products. Another example is sensitivity/specificity computations are necessary for in-vitro diagnostics, and Taguchi methods can be very useful for designing devices. Even notions of equivalence and noninferiority have different interpretations in the medical device field compared to pharmacokinetics. It contains topics such as dynamic modeling, machine learning methods, equivalence testing, and experimental design, for example.This book is for those with no statistical experience, as well as those with statistical knowledgeable¿with the hope to provide some insight into what methods are likely to help provide rationale for choices relating to data gathering and analysis activities for medical devices.

This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler¿s shape matrix.

This book explores Complex System Governance (CSG)-an emerging field concerned with the design, execution, and evolution of essential functions necessary to ensure continued viability of a system. The book focuses on three primary development areas to better understand and utilize current developments CSG. First, the conceptual foundations for CSG are developed, from systems theory, management cybernetics, and governance. Second, a set of critical CSG topics are examined from conceptual as well as practice perspectives. Third, several development and application issues are discussed. Ultimately, CSG is positioned as an emerging field with strong theoretical grounding and significant implications for improving practices and performance to better address complex systems and their problems.  

Probability theory is a branch of statistics, a science that employs mathematical methods of collection, organization, and interpretation of data, with applications in practically all scientific areas. This book provides a comprehensive overview of probability theory. It discusses some fundamental aspects of pure and applied probability theory and explores its use in solving a large array of problems. Topics addressed include complex probability, the stability of algorithms in statistical modeling, the non-homogeneous Hofmann process, and more.