Sandsynlighedsregning og statistik

I anledning af den seneste reform af læreruddannelsen er Matematik for lærerstuderende nu blevet målrettet de nye krav. Stokastik 1.-10. klasse præsenterer fagligt og fagdidaktisk materiale samt tilhørende arbejdsopgaver svarende til ét modul efter LU13. Stokastik er det, der i skolen hedder sandsynlighedsregning og statistik. Da der er stort overlap mellem kravene i undervisningsfaget matematik 1.-6. klasse og undervisningsfaget matematik 4.-10. klasse, dækker bogen begge disse faglige specialiseringer. Den såkaldte stofdidaktik, der er knyttet til bogens faglige emner, findes i særlige kapitler, mens det fagdidaktiske stof, der er fælles for al matematikundervisning, skal søges i to andre bøger i systemet: Fagdidaktikken findes i Delta, og bogen My dækker elever med særlige behov.

Statistik for ikke-statistikere er en kort introduktion til statistik. Bogen er en 2. udgave og forklarer statistikken, så den er til at forstå. Den viser konsekvent, hvad statistikken kan bruges til, og forudsætter blot, at du kan bruge en lommeregner. Den er forsynet med talrige eksempler. Den gennemgår indsamling, bearbejdning, analyse og præsentation af data. OBS! Ny udgave i oktober 2017, brug SBN 9788759329450

Statistik benyttes i forbindelse med det daglige arbejde i laboratoriet og i forbindelse med planlægning af forsøg, analyse af forsøgsresultater eller metodeudvikling. Kendskab til statistik er nødvendig for forståelsen af publiceret forskningslitteratur og i forbindelse med egen forskning. Denne bog udfylder et behov for let tilgængelig elementær statistik for bioanalytikerstuderende, bioanalytikere, læger, kemikere og andre der arbejder inden for det biomedicinske område. Bogen er tænkt som en praktisk orienteret bog. Meningen er at give læseren en forståelse af, hvilke metoder, man skal vælge, når man har nogle konkrete data at arbejde med. Det er ikke vigtigt at kunne statistiske formler udenad; dem kan man slå op. Det er vigtigt at forstå muligheder, forudsætninger, begrænsninger, og tolkningen i forbindelse med brugen af statistik. Bogens hovedvægt ligger på den parametriske statistik, men nogle af de hyppigst benyttede nonparametriske tests gennemgås også.

Denne bog er beregnet til et syv-ugers introducerende kursus i statistik. Kurset består af forelæsninger og øvelser, hvor opgaverne i bogen regnes. Det forudsættes, at deltagerne har haft et indledende matematikkursus. Bogen beskriver en række simple statistiske modeller og inferens i disse. Hver modelintroduceres gennem et datasæt og en lille baggrundshistorie. De fleste af kapitlerne afsluttes med et afsnit med titlen Testkatalog, hvor de test, der er indført i kapitlet, gengives på tabelform. Bogen blev første gang trykt i 2007 og har gennemgået flere mindre revisioner.

Introduktion til statistik med SPSS giver dig et grundigt blik ned i maskinrummet på statistikprogrammet SPSS, og du får samtidig et godt metodisk og teoretisk fundament til at kunne udføre fornuftige kvantitative analyser. Bogen er en praksisorienteret bog, som hverken kræver, at du er it-nørd eller matematik-haj for at komme i gang med at forstå og anvende statistik og SPSS."En stor force ved bogen er, at den ikke nøjes med at forklare, hvad man skal kigge efter i et output - men også forklarer hvad hele outputtet betyder. Dermed sidder man ikke med en tom følelse af bare at være sluppet igennem hvor gærdet er lavest. Man får derimod mulighed for, gennem korte og præcise, og rigt illustrerede (illustrationer fra SPSS) eksempler at følge eksempler til dørs." Stud.scient.pol Thomas Emil Jensen

Statistik med Excel omhandler statistiske analyser baseret på funktioner i regnearksprogrammet Excel (Microsoft Office). Per Vejrup-Hansen viser, hvordan man med et standardprogram som Excel kan udføre en række forskelligartede analyser af fx spørgeskema-data og tidsserier. Samtidig forklares de grundlæggende kendetegn ved de statistiske metoder. Bogen vil således også være relevant i indledende undervisning i teoretisk statistik. - Mål for skævhed og spredning i fordelinger - Test af gennemsnit i forskellige grupper: er de signifikant forskellige? herunder t-test og variansanalyse- Test af usikkerhed på proportioner eller procentandele - fx andelen af bestemte svarkategorier - Sammenligning af fordelinger af kendetegn, fx svarfordelinger i forskellige grupper (c2-test) - Korrelation og korrelationskoefficient - Regressionsanalyse, herunder bestemmelse af ikke-lineær sammenhæng mellem kvantitative variabler (tendenslinier i Excel) og anvendelse af dummy-variabler for kvalitative kendetegn.Det vises konkret, hvordan man indtaster spørgeskema-data i Excel og danner tabeller som grundlag for analyser, og der indgår opgaver til hvert kapitel i bogen. Bogen fungerer fint med Excel 2007, idet der ikke er ændringer i selve funktionerne og dataanalyser i forhold til tidligere udgaver af Excel.

En introduktion til statistikprogrammet R. Bogen introducerer brugeren for programmets basale elementer og præsenterer derefter deres anvendelse til statistisk analyse.R er et statistikprogram, der bruges og udvikles af statistikere over hele verden. Det er sandsynligvis det førende statistikprogram, i det mindste blandt statistikere, og det er gratis at anvende og frit tilgængeligt.Denne bog er rettet mod nye brugere af programmet. Med afsæt i biovidenskaberne behandler bogen gængse dataproblematikker og statistiske modeller.

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

Denne formelsamling er udarbejdet med henblik på at kunne anvendes i forbindelse med statistikundervisningen på erhvervsskolernes korte videregående uddannelser (erhvervsakademiuddannelserne ), på HD og HA, og den anvendes på andre studier med et tilsvarende statistikpensum.Formelsamlingen giver, på begrænset plads, et overblik over de metoder, der er til rådighed, når man skal løse et statistisk problem.

In A Mathematician at the Ballpark, professor Ken Ross reveals the math behind the stats. This lively and accessible book shows baseball fans how to harness the power of made predictions and better understand the game. Using real-world examples from historical and modern-day teams, Ross shows: . Why on-base and slugging percentages are more important than batting averages . How professional odds makers predict the length of a seven-game series . How to use mathematics to make smarter bets A Mathematician at the Ballpark is the perfect guide to the science of probability for the stats-obsessed baseball fans-and, with a detailed new appendix on fantasy baseball, an essential tool for anyone involved in a fantasy league.

This book narrates the detailed review on stochastic behavior of repeated purchasers and made an attempt to compare expected number of repeated purchase consumers for the experimental data. A new compound distribution with Poisson and Weibull distributions for studying the consumer behavior is presented. It¿s parameters and properties are derived. It can be used for studying the consumer behavioral distribution for varying. Further, this book emphasizes on the brand performance indicators of the Dirichlet model are used to construct a more detailed statistical model for the transition probability matrix, and this model is used to investigate Markovian characteristics. The least square principle is used to estimate the transition model parameters. The stationary probabilities are derived for each state of the Markov chain and analysis is illustrated with an example and also a detailed outline construction of Hidden Markov model is exhibited to capture the relationships, and quantifying the the consumer dynamic attitudes. The transition probability matrices derived with considering the prime factors which influence the consumer behavior with the help of two brands case.

This book focuses on the main advancements made in the economics and social sciences field through the use of grey systems theory. As a result, it addresses both the state of the art and the applications of grey systems theory in economics and social sciences. The book is structured in eight main chapters, covering the following topics: the state of the art in the grey systems theory research in economics and social sciences, which includes a bibliometric analysis, a selection of the most well-cited papers in the field, and a selection of applications in which the grey systems theory is used in the areas of suppliers selection, risk assessment, public opinion assessment, linear programming, complex projects management, social media analysis, and natural language processing Each chapter gives an overview of a particular economic or social sciences topic, providing an explanation on the main terms and methods used for solving the problem, including the notations, terminology, and the needed steps to solve it. A practical application is presented in most of the chapters, while in the others, a series of case studies are presented from the literature and discussed in depth in terms of methods used and advantages brought by each of these methods. The last chapter discusses the hybridization cases in which the grey systems theory has been or can be successfully used along with other artificial intelligence methods and techniques for a more advanced analysis in the economics and social sciences field. The reasoning and the explanations used in the book are easy to understand for the interested persons who are not familiar to the field and want to learn more related on how the grey systems theory can be applied to economics and social sciences. As for the experts in this field, this book can be a good referral point for developing new areas of research by combining the advantages of the grey systems theory with other theories within the field.

This volume presents a selection of texts that reflects the current research streams in probability, with an interest toward topics such as filtrations, Markov processes and Markov chains as well as large deviations, Stochastic Partial Differential equations, rough paths theory, quantum probabilities and percolation on graphs.The featured contributors are R. L. Karandikar and B. V. Rao, C. Leuridan, M. Vidmar, L. Miclo and P. Patie, A. Bernou, M.-E. Caballero and A. Rouault, J. Dedecker, F. Merlevède and E. Rio, F. Brosset, T. Klein, A. Lagnoux and P. Petit, C. Marinelli and L. Scarpa, C. Castaing, N. Marie and P. Raynaud de Fitte, S. Attal, J. Deschamps and C. Pellegrini, and N. Eisenbaum.

Statistical Inference (SI), as an essential chapter of Statistical Science, provides advanced methods for problem solving and decision making based on observed data. It is also an advanced part of our DATA ANALYTICS series with textbooks that present the background of concepts, statistical methods, probabilistic models and practical data-driven research problems in management, science, engineering, technology and sustainable development. SI discusses a basic coverage of key principles to state-of-the art concepts and applications. Although statistical techniques and computational methods are emphasized throughout, the book briefly has engineering and management orientations. In this write-up we try to convey honestly methodology and mathematical methods being useful in scientific domains as actuarial and financial sciences, in practical sectors as quality control, urban traffic management, environment an manufacturing. Readers, graduate students, researchers and professionals in diverse scientific exploration and engineering sectors will find that mathematical treatments and logical elucidation of many statistical results in the text are soundly accepted in their research works.

Are you above average? Is your child an A student? Is your employee an introvert or an extrovert? Every day we are measured against the yardstick of averages, judged according to how closely we come to it or how far we deviate from it.The assumption that metrics comparing us to an average?like GPAs, personality test results, and performance review ratings?reveal something meaningful about our potential is so ingrained in our consciousness that we don't even question it. That assumption, says Harvard's Todd Rose, is spectacularly?and scientifically?wrong.In The End of Average, Rose, a rising star in the new field of the science of the individual shows that no one is average. Not you. Not your kids. Not your employees. This isn't hollow sloganeering?it's a mathematical fact with enormous practical consequences. But while we know people learn and develop in distinctive ways, these unique patterns of behaviors are lost in our schools and businesses which have been designed around the mythical ?average person.? This average-size-fits-all model ignores our differences and fails at recognizing talent. It's time to change it.Weaving science, history, and his personal experiences as a high school dropout, Rose offers a powerful alternative to understanding individuals through averages: the three principles of individuality. The jaggedness principle (talent is always jagged), the context principle (traits are a myth), and the pathways principle (we all walk the road less traveled) help us understand our true uniqueness?and that of others?and how to take full advantage of individuality to gain an edge in life.Read this powerful manifesto in the ranks of Drive, Quiet, and Mindset?and you won't see averages or talent in the same way again.

This book provides a captivating journey through the realms of classical and quantum systems as it unravels the profound influence that noise may have on their static and dynamic properties. The first part of the book offers succinct yet enlightening discussions on foundational topics related to noise. The second part focuses on a variety of applications, where a diverse spectrum of noise effects in physical systems comes to life, meticulously presented and thoughtfully analyzed. Whether you are a curious student or a dedicated researcher, this book is your key to gaining invaluable insights into noise effects in physical systems. ¿The book has the merit of presenting several topics scattered in the literature and could become a very useful reference.¿ Giovanni Jona-Lasinio, Sapienza ¿ Università di Roma, Italy

This book presents the econometric foundations and applications of multi-dimensional panels, including modern methods of big data analysis. In light of the big data revolution and the emergence of higher dimensional panel data sets, it provides new results to synthesize existing knowledge on the field. The first, theoretical part of the volume is providing the econometric foundations to deal with these new high-dimensional panel data sets. It not only synthesizes our current knowledge, but mostly, presents new research results. The second empirical part of the book provides insight into the most relevant applications in this area. These chapters are a mixture of surveys and new results, always focusing on the econometric problems and feasible solutions.This second extended and revised edition provides an update of all existent chapters to reflect on new developments in the area as well as several new chapters on topics such as machine learning, nonparametric models, networks, and multi-dimensional panels in health economics. The book serves as a standard reference work, a textbook for graduate students in economics, and a source of background material for professionals conducting empirical studies.

This book is the first to focus on the global flow of funds (GFF), providing an introduction to its fundamental concepts and establishing a theoretical framework for analysis. It connects the flow of funds within domestic economies to that of the rest of the world, offering a comprehensive analysis of GFF dynamics. This study enhances GFF statistics, enabling the assessment of global financial stability from both national and cross-border sectoral perspectives. The GFF data provide valuable insights into analyzing interconnectivity across borders and an understanding of global financial interdependencies. By examining the data sources and reconstructing the statistical framework to establish the GFF statistical matrix, this book conducts a case study to evaluate financial risks and influences in G20 countries. Subsequently, it connects the GFF matrix with sectoral account data and the flow of funds to establish the sectoral from-whom-to-whom financial stock matrix (SFSM). The SFSM aims to establish a new framework for conducting multi-country, multi-sector analysis within the G20, with a special emphasis on examining the national and cross-border exposures of sectors in China, Japan, and the USA. This involves constructing country-specific financial networks and connecting them based on cross-border exposures. The systematic analysis results effectively showcase the financial interconnections among G20 countries within the GFF and shed light on the attributes of external shocks and internal influences. The focus is particularly on the changes in risk exposure between China and the USA concerning their external assets and liabilities and the implications of economic decoupling of these dynamics.

¿This book constitutes the proceedings of the 14th International Workshop on Statistical Atlases and Computational Models of the Heart, STACOM 2023, as well as the Cardiac MRI Reconstruction Challenge, CMRxRecon Challenge. There was a total of 53 submissions to the workshop. The 24 regular workshop papers included in this volume were carefully reviewed and selected from 29 paper submissions. They deal with cardiac segmentation, modelling, strain quantification, registration, statistical shape analysis, and quality control. In addition, 21 papers from the CMRxRecon challenge are included in this volume. They focus on fast CMR image reconstruction and provide a benchmark dataset that enables the broader research community to promote advances in this area of research.