Matematikprogrammer og statistikprogrammer

FACTFULNESS handler om verden, og hvordan vi kan blive bedre til at forstå den, som den virkelig er. Når man stiller folk simple spørgsmål om globale tendenser, giver de altid de forkerte svar. Hvor mange piger går for eksempel i skole? Hvor stor vil Jordens befolkning være i 2050? Og lever størstedelen i rige eller fattige lande? I FACTFULNESS viser Hans Rosling sammen med Ola Rosling og Anna Rosling Rönnlund, hvorfor misforståelserne sker. De beskriver 10 fundamentale menneskelige instinkter, som konsekvent forhindrer os i at have et faktabaseret verdenssyn. Læs denne bog, og dit syn på verden vil blive forandret for altid. "En af de vigtigste bøger jeg nogensinde har læst - en uundværlig vejledning i at tænke klart om verden." Bill Gates

BIOSTATISTIK & EPIDEMIOLOGIBag sundhedsvidenskabelige undersøgelser er indsamlet en lang række data. Det er en videnskabelig disciplin at gøre data overskuelige, håndtér- og analysérbare på korrekt vis, så sammenhænge mellem f.eks. adfærd og sundhed er til at forstå i et udsagn som: ”Mandlige rygere har 50 % større risiko for blodpropper”. Hvordan når man frem til det resultat? Og holder det?BIOSTATISTIK & EPIDEMIOLOGI yder læseren en forståelse af statistikken og epidemiologiens grundbegreber samt mulighed for at mestre basale værktøjer til beskrivelse af egne observationer. Første del af bogen er tilegnet statistiske begreber og analyser, f.eks. kategorisering af data og typer af tests, mens anden del af bogen beskæftiger sig med principperne bag forskning og studiedesigns. Undervejs kan læseren afprøve egne beregninger, teste sin viden, og bogens overskuelige struktur og grundige indeksikalisering gør den velegnet som opslagsværk og til støtte, når begreber fra videnskabelige artikler skal læses og forstås.Bogen henvender sig primært til medicinstuderende ved landets fire fakulteter i København, Odense, Aarhus og Aalborg, men andre faggrupper, såsom odontologi, farmaci, humanbiologi og folkesundhedsvidenskab, vil også finde de beskrevne principper anvendelige som introduktion til basal statistik og epidemiologi.

Learn how to use R to turn raw data into insight, knowledge, and understanding. This book introduces you to R, RStudio, and the tidyverse, a collection of R packages designed to work together to make data science fast, fluent, and fun. Suitable for readers with no previous programming experience, R for Data Science is designed to get you doing data science as quickly as possible.Authors Hadley Wickham and Garrett Grolemund guide you through the steps of importing, wrangling, exploring, and modeling your data and communicating the results. Youll get a complete, big-picture understanding of the data science cycle, along with basic tools you need to manage the details. Each section of the book is paired with exercises to help you practice what youve learned along the way.Youll learn how to:Wrangletransform your datasets into a form convenient for analysisProgramlearn powerful R tools for solving data problems with greater clarity and easeExploreexamine your data, generate hypotheses, and quickly test themModelprovide a low-dimensional summary that captures true "e;signals"e; in your datasetCommunicatelearn R Markdown for integrating prose, code, and results

This book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author¿s lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter ¿Notch Signaling in Embryology and Cancer¿, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.

This book provides a highly practical introduction to Bayesian statistical modeling with Stan, which has become the most popular probabilistic programming language.The book is divided into four parts. The first part reviews the theoretical background of modeling and Bayesian inference and presents a modeling workflow that makes modeling more engineering than art. The second part discusses the use of Stan, CmdStanR, and CmdStanPy from the very beginning to basic regression analyses. The third part then introduces a number of probability distributions, nonlinear models, and hierarchical (multilevel) models, which are essential to mastering statistical modeling. It also describes a wide range of frequently used modeling techniques, such as censoring, outliers, missing data, speed-up, and parameter constraints, and discusses how to lead convergence of MCMC. Lastly, the fourth part examines advanced topics for real-world data: longitudinal data analysis, state space models, spatial data analysis, Gaussian processes, Bayesian optimization, dimensionality reduction, model selection, and information criteria, demonstrating that Stan can solve any one of these problems in as little as 30 lines.Using numerous easy-to-understand examples, the book explains key concepts, which continue to be useful when using future versions of Stan and when using other statistical modeling tools. The examples do not require domain knowledge and can be generalized to many fields. The book presents full explanations of code and math formulas, enabling readers to extend models for their own problems. All the code and data are on GitHub.

Overview of Software EngineeringSoftware engineering is a rapidly evolving field within the realm of information technology. It encompasses the systematic development, operation, and maintenance of software systems, aiming to create reliable and efficient solutions to complex problems. This subchapter provides engineers in the information technology industry with a comprehensive overview of software engineering, highlighting its key concepts, principles, and methodologies.The chapter begins by defining software engineering and its significance in the modern world. It emphasizes the importance of software in various industries, from healthcare and finance to transportation and entertainment. Software engineering plays a critical role in developing robust, secure, and scalable solutions that meet the specific needs and requirements of businesses and end-users.Next, the subchapter explores the fundamental principles of software engineering. It delves into the software development life cycle, highlighting its different phases such as requirements gathering, analysis, design, implementation, testing, deployment, and maintenance. The chapter emphasizes the need for a systematic and iterative approach to software development, emphasizing the importance of collaboration, communication, and documentation throughout the process.Furthermore, the subchapter discusses various software engineering methodologies, including traditional waterfall, agile, and DevOps. It explains the strengths and weaknesses of each approach, helping engineers understand which methodology is best suited for their projects. It also introduces popular software development frameworks such as Scrum and Kanban, providing engineers with practical insights into managing and organizing their development teams.The subchapter also covers essential software engineering concepts such as software quality assurance, software testing, and software configuration management. It explains the importance of these concepts in ensuring the reliability, performance, and security of software systems. It also introduces engineers to various testing techniques and tools that aid in validating software functionality and identifying potential issues.

After providing an in-depth introduction to derivative-free global optimization with various constraints, this book presents new original results from well-known experts on the subject. A primary focus of this book is the well-known class of deterministic DIRECT (DIviding RECTangle)-type algorithms. This book describes a new set of algorithms derived from newly developed partitioning, sampling, and selection approaches in the box- and generally-constrained global optimization, including extensions to multi-objective optimization. DIRECT-type optimization algorithms are discussed in terms of fundamental principles, potential, and boundaries of their applicability. The algorithms are analyzed from various perspectives to offer insight into their main features. This explains how and why they are effective at solving optimization problems. As part of this book, the authors also present several techniques for accelerating the DIRECT-type algorithms through parallelization and implementing efficient data structures by revealing the pros and cons of the design challenges involved. A collection of DIRECT-type algorithms described and analyzed in this book is available in DIRECTGO, a MATLAB toolbox on GitHub. Lastly, the authors demonstrate the performance of the algorithms for solving a wide range of global optimization problems with various constraints ranging from a few to hundreds of variables.Additionally, well-known practical problems from the literature are used to demonstrate the effectiveness of the developed algorithms. It is evident from these numerical results that the newly developed approaches are capable of solving problems with a wide variety of structures and complexity levels.Since implementations of the algorithms are publicly available, this monograph is full of examples showing how to use them and how to choose the most efficient ones, depending on the nature of the problem being solved. Therefore, many specialists, students, researchers, engineers, economists, computer scientists, operations researchers, and others will find this book interesting and helpful.

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.

Numerical simulation is a powerful tool used in various fields of science and engineering to model complex systems and predict their behavior. It involves developing mathematical models that describe the behavior of a system and using computer algorithms to solve these models numerically. By doing so, researchers and engineers can study the behavior of a system in detail, which may only be possible with analytical methods. Numerical simulation has many advantages over traditional analytical methods. It allows researchers and engineers to study complex systems¿ behavior in detail and predict their behavior in different scenarios. It also allows for the optimization of systems and the identification of design flaws before they are built. However, numerical simulation has its limitations. It requires significant computational resources, and the accuracy of the results depends on the quality of the mathematical models and the discretization methods used. Nevertheless, numerical simulation remains a valuable tool in many fields and its importance is likely to grow as computational resources become more powerful and widely available. Numerical simulation is widely used in physics, engineering, computer science, and mathematics. In physics, for example, numerical simulation is used to study the behavior of complex systems such as weather patterns, fluid dynamics, and particle interactions. In engineering, it is used to design and optimize systems such as aircraft, cars, and buildings. In computer science, numerical simulation models and optimization algorithms and data structures. In mathematics, it is used to study complex mathematical models and to solve complex equations. This book familiarizes readers with the practical application of the numerical simulation technique to solve complex analytical problems in different industries and sciences.

Bayes Factors for Forensic Decision Analyses with R provides a self-contained introduction to computational Bayesian statistics using R. With its primary focus on Bayes factors supported by data sets, this book features an operational perspective, practical relevance, and applicability¿keeping theoretical and philosophical justifications limited. It offers a balanced approach to three naturally interrelated topics:Probabilistic Inference - Relies on the core concept of Bayesian inferential statistics, to help practicing forensic scientists in the logical and balanced evaluation of the weight of evidence.Decision Making - Features how Bayes factors are interpreted in practical applications to help address questions of decision analysis involving the use of forensic science in the law.Operational Relevance - Combines inference and decision, backed up with practical examples and complete sample code in R, including sensitivity analyses and discussion on how to interpret results in context.Over the past decades, probabilistic methods have established a firm position as a reference approach for the management of uncertainty in virtually all areas of science, including forensic science, with Bayes' theorem providing the fundamental logical tenet for assessing how new information¿scientific evidence¿ought to be weighed. Central to this approach is the Bayes factor, which clarifies the evidential meaning of new information, by providing a measure of the change in the odds in favor of a proposition of interest, when going from the prior to the posterior distribution. Bayes factors should guide the scientist's thinking about the value of scientific evidence and form the basis of logical and balanced reporting practices, thus representing essential foundations for rational decision making under uncertainty.This book would be relevant to students, practitioners, and applied statisticiansinterested in inference and decision analyses in the critical field of forensic science. It could be used to support practical courses on Bayesian statistics and decision theory at both undergraduate and graduate levels, and will be of equal interest to forensic scientists and practitioners of Bayesian statistics for driving their evaluations and the use of R for their purposes.This book is Open Access.

This textbook presents methods and techniques for time series analysis and forecasting and shows how to use Python to implement them and solve data science problems. It covers not only common statistical approaches and time series models, including ARMA, SARIMA, VAR, GARCH and state space and Markov switching models for (non)stationary, multivariate and financial time series, but also modern machine learning procedures and challenges for time series forecasting. Providing an organic combination of the principles of time series analysis and Python programming, it enables the reader to study methods and techniques and practice writing and running Python code at the same time. Its data-driven approach to analyzing and modeling time series data helps new learners to visualize and interpret both the raw data and its computed results. Primarily intended for students of statistics, economics and data science with an undergraduate knowledge of probability and statistics, the book will equally appeal to industry professionals in the fields of artificial intelligence and data science, and anyone interested in using Python to solve time series problems.

Geophysical Data Analysis and Inverse Theory with MATLAB or Python, Fifth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. The book demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention given to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. A series of "crib sheets" offer step-by-step summaries of methods presented. Utilizing problems and case studies, along with MATLAB and Python computer code and summaries of methods, the book provides professional geophysicists, students, data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.

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.

Learn how to use R for everything from workload automation and creating online reports, to interpreting data, map making, and more.Written by the founder of a very popular online training platform for the R programming language!The R programming language is a remarkably powerful tool for data analysis and visualization, but its steep learning curve can be intimidating for some. If you just want to automate repetitive tasks or visualize your data, without the need for complex math, R for the Rest of Us is for you.Inside you’ll find a crash course in R, a quick tour of the RStudio programming environment, and a collection of real-word applications that you can put to use right away. You’ll learn how to create informative visualizations, streamline report generation, and develop interactive websites—whether you’re a seasoned R user or have never written a line of R code.You’ll also learn how to:• Manipulate, clean, and parse your data with tidyverse packages like dplyr and tidyr to make data science operations more user-friendly• Create stunning and customized plots, graphs, and charts with ggplot2 to effectively communicate your data insights• Import geospatial data and write code to produce visually appealing maps automatically• Generate dynamic reports, presentations, and interactive websites with R Markdown and Quarto that seamlessly integrate code, text, and graphics• Develop custom functions and packages tailored to your specific needs, allowing you to extend R’s functionality and automate complex tasksUnlock a treasure trove of techniques to transform the way you work. With R for the Rest of Us, you’ll discover the power of R to get stuff done. No advanced statistics degree required.

Embark on a compelling mathematical journey that seamlessly transitions from the continuous domain of algebra, differential equations, and analog electronics to discover vital connections with their discrete counterparts: integer equations, difference equations, and digital electronics. While a familiarity with differential equations and analog electronics can certainly enrich the experience, it is not a prerequisite. By leveraging a foundation in continuous mathematics, this book skillfully navigates a diverse array of discrete subjects within a remarkably efficient timeframe, all the while nurturing a solid grasp of the underlying principles.Immerse yourself in an enthralling expedition through modulus equations, the harmonies of music theory, the intricacies of integer equations, the dance of difference equations, the enigmatic Mandelbrot set, the transformative power of Z transforms, the subtleties of sampling theory, the evolution of analog to digital converters, the delicate craftsmanship of digital filters, and the captivating realm of digital communications. Despite the apparent diversity of these topics, they share a common thread of foundational mathematics that unites them.Harmonizing practical applications with theoretical principles, "From Continuous to Discrete" offers effective methodologies for solving real-world problems while still providing a robust theoretical foundation that supports these methods.

Business Analytics: Solving Business Problems with R offers a practical, hands-on introduction to analytical methods, including machine learning in real-world business scenarios. Connecting business decisions and analytical methods across multiple fields, this book guides readers through a wide range of business problems and their fitting analytical solutions, offering examples and implementation using R.

This textbook offers a comprehensive, up-to-date introduction to the Optimization Programming Language (OPL). Embedded in the IBM ILOG CPLEX Optimization Studio with its solver engine CPLEX, OPL has been popular for years not only for academic and scientific purposes, but also among practitioners who need to model and solve large-scale real-world business optimization problems. The book covers the recent features of the software and includes ten consecutive tutorials, each with additional exercises, as well as several comprehensive application studies.The book is specifically designed for advanced undergraduate and graduate courses in e.g. management science, operations research, computer science, mathematics, mathematical economics, and industrial engineering. It can also serve as self-study material for practitioners whose work involves the modeling and optimization of planning and decision problems and who need a sound introduction to the software.Solutions to the exercises as well as the source codes from the textbook are available for download (weblink included).

This book focuses on methods and models in classification and data analysis and presents real-world applications at the interface with data science. Numerous topics are covered, ranging from statistical inference and modelling to clustering and factorial methods, and from directional data analysis to time series analysis and small area estimation. The applications deal with new developments in a variety of fields, including medicine, finance, engineering, marketing, and cyber risk.The contents comprise selected and peer-reviewed contributions presented at the 13th Scientific Meeting of the Classification and Data Analysis Group of the Italian Statistical Society, CLADAG 2021, held (online) in Florence, Italy, on September 9¿11, 2021. CLADAG promotes advanced methodological research in multivariate statistics with a special focus on data analysis and classification, and supports the exchange and dissemination of ideas, methodological concepts, numerical methods, algorithms, and computational and applied results at the interface between classification and data science.

This textbook summarizes the different statistical, scientific, and financial data analysis methods for users ranging from a high school level to a professional level. It aims to combine the data analysis methods using three different programs¿Microsoft Excel, SPSS, and MATLAB. The book combining the different data analysis tools is a unique approach. The book presents a variety of real-life problems in data analysis and machine learning, delivering the best solution. Analysis methods presented in this book include but are not limited to, performing various algebraic and trigonometric operations, regression modeling, and correlation, as well as plotting graphs and charts to represent the results. Fundamental concepts of applied statistics are also explained here, with illustrative examples. Thus, this book presents a pioneering solution to help a wide range of students, researchers, and professionals learn data processing, interpret different findings derived from the analyses,and apply them to their research or professional fields. The book also includes worked examples of practical problems. The primary focus behind designing these examples is understanding the concepts of data analysis and how it can solve problems. The chapters include practice exercises to assist users in enhancing their skills to execute statistical analysis calculations using software instead of relying on tables for probabilities and percentiles in the present world.

This book provides a friendly introduction to the paradigm and proposes a broad panorama of killing applications of the Infinity Computer in optimization: radically new numerical algorithms, great theoretical insights, efficient software implementations, and interesting practical case studies. This is the first book presenting to the readers interested in optimization the advantages of a recently introduced supercomputing paradigm that allows to numerically work with different infinities and infinitesimals on the Infinity Computer patented in several countries. One of the editors of the book is the creator of the Infinity Computer, and another editor was the first who has started to use it in optimization. Their results were awarded by numerous scientific prizes. This engaging book opens new horizons for researchers, engineers, professors, and students with interests in supercomputing paradigms, optimization, decision making, game theory, and foundations of mathematics and computer science."e;Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... "e;MIT Technology Review"e;These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used."e; A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing."e;I am sure that the new approach ... will have a very deep impact both on Mathematics and Computer Science."e; D. Trigiante, Computational Management Science."e;Within the grossone framework, it becomes feasible to deal computationally with infinite quantities, in a way that is both new (in the sense that previously intractable problems become amenable to computation) and natural"e;. R. Gangle, G. Caterina, F. Tohme, Soft Computing."e;The computational features offered by the Infinity Computer allow us to dynamically change the accuracy of representation and floating-point operations during the flow of a computation. When suitably implemented, this possibility turns out to be particularly advantageous when solving ill-conditioned problems. In fact, compared with a standard multi-precision arithmetic, here the accuracy is improved only when needed, thus not affecting that much the overall computational effort."e; P. Amodio, L. Brugnano, F. Iavernaro & F. Mazzia, Soft Computing