Dieses Buch fuhrt anwendungsorientiert in die Beschreibende und Schliessende Statistik, in die Wahrscheinlichkeitsrechnung und in die Stochastische Modellierung ein und wendet sich insbesondere an Studierende der Informatik, des Ingenieur- und Wirtschaftsingenieurwesens sowie der Wirtschaftswissenschaften. Es ist ein idealer Begleiter zu jeder einsemestrigen Grundvorlesung in Statistik: Die Autoren stellen die wesentlichen Inhalte und Aspekte in kurzer und pragnanter Form dar und verzichten bewusst auf ausfuhrliche Motivationen. Zur UEberprufung des eigenen Wissens stehen Beispielaufgaben mit detaillierten Loesungen zur Verfugung. Die durchgesehene Neuauflage wurde um etwa 50 Multiple-Choice-Fragen erweitert. Diese koennen mit der Springer-Nature-Flashcards-App kostenlos heruntergeladen und interaktiv genutzt werden und sind auszugsweise auch im Buch enthalten. Auf diese Weise kann das eigene Verstandnis der Inhalte getestet werden.

Dieses Lehrbuch fuhrt in 16 einheitlich gegliederten Kapiteln in die Wahrscheinlichkeitstheorie und Statistik ein. Dabei sind die Lernziele und benoetigten Vorkenntnisse jeweils angegeben und erleichtern in Kombination mit pragnanten Zusammenfassungen die Orientierung je Kapitel. Dank vieler durchgerechneter Beispiele und UEbungsaufgaben mit Loesungen kann das Buch gut zum Selbststudium oder als Begleitliteratur zur Vorlesung verwendet werden. Nach einer sorgfaltigen Einfuhrung der Grundlagen geben weiterfuhrende Kapitel spannende Ausblicke in Anwendungsbereiche der Stochastik und der stochastischen Modellierung - etwa Markov-Ketten, stochastische Algorithmen, Warteschlangen und Monte-Carlo-Simulationen. Leserinnen und Leser erhalten so ein solides mathematisches Fundament, um die Stochastik im weiteren Studium und in der Praxis auch in komplexen Situationen anwenden zu koennen. Das Buch richtet sich an Studierende der Informatik und technischer Fachrichtungen ab dem dritten Studiensemester. Dozenten liefert es eine passgenaue Auswahl fur eine einsemestrige Vorlesung.

This practical guide is designed for students and researchers with an existing knowledge of R who wish to learn how to apply it in an epidemiological context and exploit its versatility. It also serves as a broader introduction to the quantitative aspects of modern practical epidemiology. The standard tools used in epidemiology are described and the practical use of R for these is clearly explained and laid out. R code examples, many with output, are embedded throughout the text. The entire code is also available on the companion website so that readers can reproduce all the results and graphs featured in the book. Epidemiology with R is an advanced textbook suitable for senior undergraduate and graduate students, professional researchers, and practitioners in the fields of human and non-human epidemiology, public health, veterinary science, and biostatistics.

Dieses Buch verschafft Ihnen einen UEberblick uber einige der bekanntesten Verfahren des maschinellen Lernens aus der Perspektive der mathematischen Statistik. Nach der Lekture kennen Sie die jeweils gestellten Forderungen an die Daten sowie deren Vor- und Nachteile und sind daher in der Lage, fur ein gegebenes Problem ein geeignetes Verfahren vorzuschlagen. Beweise werden nur dort ausfuhrlich dargestellt oder skizziert, wo sie einen didaktischen Mehrwert bieten - ansonsten wird auf die entsprechenden Fachartikel verwiesen. Fur die praktische Anwendung ist ein genaueres Studium des jeweiligen Verfahrens und der entsprechenden Fachliteratur noetig, zu der Sie auf Basis dieses Buchs aber schnell Zugang finden. Das Buch richtet sich an Studierende der Mathematik hoeheren Semesters, die bereits Vorkenntnisse in Wahrscheinlichkeitstheorie besitzen. Behandelt werden sowohl Methoden des Supervised Learning und Reinforcement Learning als auch des Unsupervised Learning. Der Umfang entspricht einer einsemestrigen vierstundigen Vorlesung. Die einzelnen Kapitel sind weitestgehend unabhangig voneinander lesbar, am Ende jedes Kapitels kann das erworbene Wissen anhand von UEbungsaufgaben und durch Implementierung der Verfahren uberpruft werden. Quelltexte in der Programmiersprache R stehen auf der Springer-Produktseite zum Buch zur Verfugung.

Studies of evolution at the molecular level have experienced phenomenal growth in the last few decades, due to rapid accumulation of genetic sequence data, improved computer hardware and software, and the development of sophisticated analytical methods. The flood of genomic data has generated an acute need for powerful statistical methods and efficient computational algorithms to enable their effective analysis and interpretation. Molecular Evolution: a statistical approach presents and explains modern statistical methods and computational algorithms for the comparative analysis of genetic sequence data in the fields of molecular evolution, molecular phylogenetics, statistical phylogeography, and comparative genomics. Written by an expert in the field, the book emphasizes conceptual understanding rather than mathematical proofs. The text is enlivened with numerous examples of real data analysis and numerical calculations to illustrate the theory, in addition to the working problems at the end of each chapter. The coverage of maximum likelihood and Bayesian methods are in particular up-to-date, comprehensive, and authoritative. This advanced textbook is aimed at graduate level students and professional researchers (both empiricists and theoreticians) in the fields of bioinformatics and computational biology, statistical genomics, evolutionary biology, molecular systematics, and population genetics. It will also be of relevance and use to a wider audience of applied statisticians, mathematicians, and computer scientists working in computational biology.

Learn statistical methods quickly and easily with the discovery method
With its emphasis on the discovery method, this publication encourages readers to discover solutions on their own rather than simply copy answers or apply a formula by rote. Readers quickly master and learn to apply statistical methods, such as bootstrap, decision trees, t-test, and permutations to better characterize, report, test, and classify their research findings. In addition to traditional methods, specialized methods are covered, allowing readers to select and apply the most effective method for their research, including:
* Tests and estimation procedures for one, two, and multiple samples
* Model building
* Multivariate analysis
* Complex experimental design
Throughout the text, Microsoft Office Excel(r) is used to illustrate new concepts and assist readers in completing exercises. An Excel Primer is included as an Appendix for readers who need to learn or brush up on their Excel skills.
Written in an informal, highly accessible style, this text is an excellent guide to descriptive statistics, estimation, testing hypotheses, and model building. All the pedagogical tools needed to facilitate quick learning are provided:
* More than 100 exercises scattered throughout the text stimulate readers' thinking and actively engage them in applying their newfound skills
* Companion FTP site provides access to all data sets discussed in the text
* An Instructor's Manual is available upon request from the publisher
* Dozens of thought-provoking questions in the final chapter assist readers in applying statistics to solve real-life problems
* Helpful appendices include an index to Excel and Excel add-in functions
This text serves as an excellent introduction to statistics for students in all disciplines. The accessible style and focus on real-life problem solving are perfectly suited to both students and practitioners.

Dieses Lehrbuch stellt eine Vielzahl von Werkzeugen zur Analyse von Experimenten zur Verfugung: Es zeigt die Grundlagen der Auswertung faktorieller Versuchsplane mittels ein- oder mehrfaktorieller Varianzanalysen (ANOVA) sowie mittels gangiger nichtparametrischer Alternativen. Daruber hinaus werden auch Verfahren zur UEberprufung der Annahmen von Varianzanalysen vorgestellt. Die einzelnen Verfahren werden zunachst anhand ubersichtlicher Beispiele und Datensatze motiviert, vorgestellt und mit Papier und Stift durchgerechnet. Fur groessere Beispiele kommt die frei verfugbare statistische Software R zum Einsatz, mit der die manuellen Berechnungen nachvollzogen und schliesslich auch groessere Datensatze ausgewertet werden koennen.

This book constitutes the refereed proceedings of the 9th International Conference on Optimization and Applications, OPTIMA 2018, held in Petrovac, Montenegro, in October 2018.The 35 revised full papers and the one short paper presented were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections on mathematical programming; combinatorial and discrete optimization; optimal control; optimization in economy, finance and social sciences; applications.

Carry out a variety of advanced statistical analyses including generalized additive models, mixed effects models, multiple imputation, machine learning, and missing data techniques using R. Each chapter starts with conceptual background information about the techniques, includes multiple examples using R to achieve results, and concludes with a case study. Written by Matt and Joshua F. Wiley, Advanced R Statistical Programming and Data Models shows you how to conduct data analysis using the popular R language. You'll delve into the preconditions or hypothesis for various statistical tests and techniques and work through concrete examples using R for a variety of these next-level analytics. This is a must-have guide and reference on using and programming with the R language. What You'll Learn Conduct advanced analyses in R including: generalized linear models, generalized additive models, mixed effects models, machine learning, and parallel processing Carry out regression modeling using R data visualization, linear and advanced regression, additive models, survival / time to event analysis Handle machine learning using R including parallel processing, dimension reduction, and feature selection and classification Address missing data using multiple imputation in R Work on factor analysis, generalized linear mixed models, and modeling intraindividual variability Who This Book Is For Working professionals, researchers, or students who are familiar with R and basic statistical techniques such as linear regression and who want to learn how to use R to perform more advanced analytics. Particularly, researchers and data analysts in the social sciences may benefit from these techniques. Additionally, analysts who need parallel processing to speed up analytics are given proven code to reduce time to result(s).

Der neuartige Einstieg in Digitale Medien fur die Mathematikdidaktik der Sekundarstufen, keine (zu) enge Bindung an spezifische Hard- oder Software Systematische und umfassende Darstellung von Grund auf mit Anregungen fur den Mathematikunterricht, gezielt fur das Lehramtsstudium und die Schulpraxis Die vielfaltigen Erprobungen an der Universitat Bielefeld, am Studienseminar Hamm und in der Lehrerfortbildung bilden eine gute Grundlage fur den Erfolg dieses Bandes

Das Programmpaket SAS hat sich im Lauf der Jahre als Standardprogramm zur statistischen Datenanalyse etabliert. Der souverane Umgang mit statistischen Methoden und deren praktischer Umsetzung in SAS bietet somit einen unschatzbaren Vorteil fur die tagliche Arbeit des Datenanalytikers. Im vorliegenden Buch erlernt der Leser zunachst die Grundlagen fur die Programmierung. Anschliessend wird eine grosse Auswahl statistischer Verfahren und deren Umsetzung als SAS-Programm vorgestellt. Dabei wird grosses Augenmerk auf die grafischen Aspekte der statistischen Datenanalyse gelegt. Ein zusatzlicher Teil uber Programmierung mit IML und Makros sowie hilfreiche Assistenten in SAS runden die Darstellung ab. Mit seiner umfassenden Themenauswahl ist das Buch als Einfuhrung, aber auch als Nachschlagewerk fur den fortgeschritteneren Leser geeignet.

This easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer experiments using MATLAB, Python, Maple, and Java applets. This fully updated and expanded new edition also features an even greater number of programming exercises. Topics and features: describes the fundamental concepts in analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives, integrals, and curves; discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes added material on hyperbolic functions, curves and surfaces in space, second-order differential equations, and the pendulum equation (NEW); contains experiments, exercises, definitions, and propositions throughout the text; supplies programming examples in Python, in addition to MATLAB (NEW); provides supplementary resources at an associated website, including Java applets, code source files, and links to interactive online learning material. Addressing the core needs of computer science students and researchers, this clearly written textbook is an essential resource for undergraduate-level courses on numerical analysis, and an ideal self-study tool for professionals seeking to enhance their analysis skills.

Dieses Lehrbuch motiviert und erklart die Inhalte der deskriptiven und induktiven Statistik, indem es die mathematischen Grundlagen der Statistik mit vielfaltigen, leicht nachvollziehbaren Anwendungen und Beispielen verbindet: Durch uberschaubare Beispiele, die mit Papier und Stift durchgerechnet werden koennen (und sollten!) gewinnt der Leser zunachst Verstandnis und einen routinierten Umgang mit den zentralen Formeln. Fur groessere Beispiele kommt das frei verfugbare statistische Software R zum Einsatz, welches die Berechnungen schnell und verlasslich auch fur grosse Datensatze umsetzt.

The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Levy processes or fractional Brownian motion, as well as CARMA, COGARCH, and Point processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these processes have been originally proposed in physics and more recently in finance, they are becoming popular also in biology due to the fact the time course experimental data are now available. The YUIMA package, available on CRAN, can be freely downloaded and this companion book will make the user able to start his or her analysis from the first page.

This is the first book to present time series analysis using the SAS Enterprise Guide software. It includes some starting background and theory to various time series analysis techniques, and demonstrates the data analysis process and the final results via step-by-step extensive illustrations of the SAS Enterprise Guide software. This book is a practical guide to time series analyses in SAS Enterprise Guide, and is valuable resource that benefits a wide variety of sectors.

R is now the most widely used statistical package/language in university statistics departments and many research organisations. Its great advantages are that for many years it has been the leading-edge statistical package/language and that it can be freely downloaded from the R web site. Its cooperative development and open code also attracts many contributors meaning that the modelling and data analysis possibilities in R are much richer than in GLIM4, and so the R edition can be substantially more comprehensive than the GLIM4 edition of Statistical Modelling. This text provides a comprehensive treatment of the theory of statistical modelling in R with an emphasis on applications to practical problems and an expanded discussion of statistical theory. A wide range of case studies is provided, using the normal, binomial, Poisson, multinomial, gamma, exponential and Weibull distributions, making this book ideal for graduates and research students in applied statistics and a wide range of quantitative disciplines.

Schwerpunkt auf Simulation und grafischer Darstellung der Resultate Angereichert mit Praxisbeispielen und Reflexionsaufgaben Datensatze, Programmcodes und Loesungen online verfugbar

Dieses Buch liefert Anfangern einen leichten Einstieg in SPSS und dient erfahrenen Nutzern (auch fruherer Programmversionen) zugleich als hervorragendes Nachschlagewerk. Die Nutzung des Buchs ist dabei weitgehend ohne mathematische Vorkenntnisse moeglich. Die Methoden und deren Anwendung mit SPSS werden anschaulich anhand von Beispielen aus der Praxis erlautert. Auf der Internetseite zum Buch sind alle Datensatze, erganzende Texte, UEbungsaufgaben mit ihren Loesungen sowie weitere Informationen verfugbar. Die 9. Auflage dieses Buchs basiert auf IBM SPSS Statistics 24 (Base und Exact Tests). Im Rahmen der Neuauflage wurden etliche Kapitel uberarbeitet. Hinzugekommen sind Kapitel zu neuen statistischen Verfahren sowie ein UEbersichtskapitel zu Signifikanztests: Letzteres erleichtert es dem SPSS-Nutzer, aus der Vielzahl der in SPSS verfugbaren Tests den fur seine Aufgabenstellung richtigen zu wahlen.

Building SPSS Graphs to Understand Data is for anyone needing to understand large or small amounts of data. It describes how to build and interpret graphs, showing how understanding data means that the graph must clearly and succinctly answer questions about the data. In 16 of the 19 chapters research questions are presented, and the reader builds the appropriate graph needed to answer the questions. This handy guide can be used in conjunction with any introductory or intermediate statistics book where the focus is on in-depth presentation of how graphs are used. This book will also useful for graduate students doing research at the masters or doctoral level. The book also contains a chapter designed to address many of the ways that graphs can be used to mislead the graph reader.

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages and modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses-natural deduction-is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts:
Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words.
Part II "Formal Syntactic Proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle.
Part III "Formal Semantic Disproof" shows you how to construct mathematical counterexamples to shoe that proof is impossible. Jape can check the counterexamples you build.
Part IV" Program Specification and Proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows.
Aimed at undergraduates and graduates in computer science, logic, mathematics and philosophy, thetext includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential
and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages and modern-day programming. This book concentrates on using logic as a tool: making and using formal proofs and
disproofs of particular logical claims. The logic it uses-natural deduction-is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts:
Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words.
Part II "Formal Syntactic Proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle.
Part III "Formal Semantic Disproof" shows you how to construct mathematical counterexamples to shoe that proof is impossible. Jape can check the counterexamples you build.
Part IV" Program Specification and Proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows.
Aimed at undergraduates and graduates in computer science, logic, mathematics and philosophy, thetext includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the
web.

Dieses Buch bietet einen historisch orientierten Einstieg in die Algorithmik, also die Lehre von den Algorithmen, in Mathematik, Informatik und daruber hinaus. Besondere Merkmale und Zielsetzungen sind: Elementaritat und Anschaulichkeit, die Berucksichtigung der historischen Entwicklung, Motivation der Begriffe und Verfahren anhand konkreter, aussagekraftiger Beispiele unter Einbezug moderner Werkzeuge (Computeralgebrasysteme, Internet). Als Zusatzmedien werden computer- und internetspezifische Interaktions- und Visualisierungsmoeglichkeiten (kostenlos) zur Verfugung gestellt. Das Werk wendet sich an Studierende und Lehrende an Schulen und Hochschulen sowie an Nichtspezialisten, die an den Themen "Computer/Algorithmen/Programmierung" einschliesslich ihrer historischen und geisteswissenschaftlichen Dimension interessiert sind.

Berthold Heinrich stellt die mathematischen und zeichnerischen Grundlagen fur die Darstellung von Objekten im Raum auf kariertem Papier vor. Dabei prasentiert er auch die Nutzung von Software. In der Schule wird oft kariertes Papier als Raster zur Darstellung von Flachen und Koerpern genutzt. Allerdings werden, selbst in einigen Druckwerken, z.B. die entstehenden Ellipsen und Winkelboegen ungenau gezeichnet oder eine Kugelkontur falsch als Kreis dargestellt. Im vorliegenden Essential werden die korrekten Verfahren sowohl theoretisch als auch an konkreten Beispielen vorgestellt und koennen meist direkt umgesetzt werden. Einige aufwandigere Ablaufe stellt der Autor anschaulich an Beispielen dar.

This textbook introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked-out problems. Each section starts with a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate the use of new commands in Mathematica whilst solving each problem presented; - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations; and - the third presents more challenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students of mathematics, science, engineering and finance, the book also includes chapters on calculus and solving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problem solving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computational tool. This new edition has been extensively revised and updated, and includes new chapters with problems and worked examples.