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.

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.

The Instant New York Times Bestseller“Engaging and entertaining… a glimpse of the economy of the future.” —Tim Wu, New York Times Book ReviewFrom the New York Times bestselling author of The Signal and the Noise, the definitive guide to our era of risk—and the players raising the stakes   In the bestselling The Signal and the Noise, Nate Silver showed how forecasting would define the age of Big Data. Now, in this timely and riveting new book, Silver investigates “the River,” the community of like-minded people whose mastery of risk allows them to shape—and dominate—so much of modern life. These professional risk-takers—poker players and hedge fund managers, crypto true believers and blue-chip art collectors—can teach us much about navigating the uncertainty of the twenty-first century. By immersing himself in the worlds of Doyle Brunson, Peter Thiel, Sam Bankman-Fried, Sam Altman, and many others, Silver offers insight into a range of issues that affect us all, from the frontiers of finance to the future of AI. Most of us don’t have traits commonly found in the River: high tolerance for risk, appreciation of uncertainty, affinity for numbers—paired with an instinctive distrust of conventional wisdom and a competitive drive so intense it can border on irrational. For those in the River, complexity is baked in, and the work is how to navigate it. People in the River have increasing amounts of wealth and power in our society, and understanding their mindset—and the flaws in their thinking— is key to understanding what drives technology and the global economy today. Taking us behind the scenes from casinos to venture capital firms, and from the FTX inner sanctum to meetings of the effective altruism movement, On the Edge is a deeply reported, all-access journey into a hidden world of power bro­kers and risk-takers.

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.

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

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.Bogen er en del af MEDICINSK FORSKNING-serien, hvis formål er at udbrede forståelsen for teorier relateret til medicinsk forskning og bidrage med faglig viden af højeste kvalitet. Andre bøger i serien inkluderer 22 TEMATEORIER TIL KVALITATIV FORSKNING og FORSKNING I SUNDHED.

Endelig en statistikgrundbog, der hverken er kedelig eller svær at komme igennem. Med stor sandsynlighed dækker pensum for grundlæggende statistik på de fleste videregående uddannelser og er særligt skrevet til merkantile erhvervsakademiuddannelser.Med stor sandsynlighed fokuserer på statistikkens formål og anvendelse – både på studiet og i hverdagen. Du får gode eksempler på, og tips til, hvordan du bruger Excel til statistiske analyser, og du kan downloade de datasæt, der bruges i bogen, for selv at prøve dem af.Bogen vil gerne gøre det sværeste nemmere. Derfor lægger den særlig vægt på forståelsen og brugen af formler, og den indeholder mange eksempler. Ved hjælp af navigationsfigurer og redskaber får du et overblik over den grundlæggende statistik. Når du har læst denne bog, vil du kunne matche statistiske problemstillinger med de rette metoder og forstå de mange anvendelsesmuligheder.Om forfatteren: Majbritt Skov er partner og cheføkonom hos Deloitte. Siden 2003 har hun undervist i statistik og erhvervsøkonomisk metode på HD- og universitetsniveau.

"From the New York Times bestselling author of The Signal and the Noise, the definitive guide to our era of risk-and the players raising the stakes In the bestselling The Signal and the Noise, Nate Silver showed how forecasting would define the age of Big Data. Now, in this timely and riveting new book, Silver investigates "The River," or those whose mastery of risk allows them to shape-and dominate-so much of modern life. These professional risk takers-poker players and hedge fund managers, crypto true-believers and blue-chip art collectors-can teach us much about navigating the uncertainty of the 21st century. By embedding within the worlds of Doyle Brunson, Peter Thiel, Sam Bankman-Fried, Sam Altman, and many others, Silver offers insight into a range of issues that affect us all, from the frontiers of finance to the future of AI. The River has increasing amounts of wealth and power in our society, and understanding their mindset-including the flaws in their thinking-is key to understanding what drives technology and the global economy today. There are certain commonalities in this otherwise diverse group: high tolerance for risk; appreciation of uncertainty; affinity for numbers; skill at de-coupling; self-reliance and a distrust of the conventional wisdom. For the River, complexity is baked in, and the work is how to navigate it, without going beyond the pale. Taking us behind-the-scenes from casinos to venture capital firms to the FTX inner sanctum to meetings of the effective altruism movement, On the Edge is a deeply-reported, all-access journey into a hidden world of powerbrokers and risk takers"--

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.

Statistical Analysis for Civil Engineers: Mathematical Theory and Applied Experiment Design is a well-researched and topically organized reference book that guides its readers, both in academia and industry, to recognize how to describe unpredictable events in a quantitative way and to learn how these events can be incorporated into practical engineering analysis that facilitates data-driven problem solving and optimization-based decision-making.Written by experts in the field with a proven track record as educators and practicing consultancy specialists, this book has been developed in such a manner that it advances understanding of the mathematical theory underlying analytical methodology gradually. It also supports practical application through relevant worked examples in a variety of civil engineering branches, notably structural, materials, transportation, and geotechnical engineering. Through all stages of data analysis, numerical modeling and simulation, and implementation, the volume emphasizes the need to change the current perception with respect to the use of modern statistical techniques in the scientific as well as practical spheres of civil engineering.

¿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.

This book reports on cutting-edge theories and methods for analyzing complex systems, such as transportation and communication networks and discusses multi-disciplinary approaches to dependability problems encountered when dealing with complex systems in practice. The book presents the most relevant findings discussed at the 23rd International Multidisciplinary Conference on Reliability and Statistics in Transportation and Communication (RelStat 2023), which took place as a hybrid event on October 19 ¿ 21, 2023, in/from Riga, Latvia. It spans a broad spectrum of advanced theories and methods, giving a special emphasis to the digitalization of transport systems, as well as smart, artificial intelligence, and digital twins applications.

Learn the fundamentals of Bayesian modeling using state-of-the-art Python libraries, such as PyMC, ArviZ, Bambi, and more, guided by an experienced Bayesian modeler who contributes to these librariesKey Features- Conduct Bayesian data analysis with step-by-step guidance- Gain insight into a modern, practical, and computational approach to Bayesian statistical modeling- Enhance your learning with best practices through sample problems and practice exercises- Purchase of the print or Kindle book includes a free PDF eBook.Book DescriptionThe third edition of Bayesian Analysis with Python serves as an introduction to the main concepts of applied Bayesian modeling using PyMC, a state-of-the-art probabilistic programming library, and other libraries that support and facilitate modeling like ArviZ, for exploratory analysis of Bayesian models; Bambi, for flexible and easy hierarchical linear modeling; PreliZ, for prior elicitation; PyMC-BART, for flexible non-parametric regression; and Kulprit, for variable selection.In this updated edition, a brief and conceptual introduction to probability theory enhances your learning journey by introducing new topics like Bayesian additive regression trees (BART), featuring updated examples. Refined explanations, informed by feedback and experience from previous editions, underscore the book's emphasis on Bayesian statistics. You will explore various models, including hierarchical models, generalized linear models for regression and classification, mixture models, Gaussian processes, and BART, using synthetic and real datasets.By the end of this book, you will possess a functional understanding of probabilistic modeling, enabling you to design and implement Bayesian models for your data science challenges. You'll be well-prepared to delve into more advanced material or specialized statistical modeling if the need arises.What you will learn- Build probabilistic models using PyMC and Bambi- Analyze and interpret probabilistic models with ArviZ- Acquire the skills to sanity-check models and modify them if necessary- Build better models with prior and posterior predictive checks- Learn the advantages and caveats of hierarchical models- Compare models and choose between alternative ones- Interpret results and apply your knowledge to real-world problems- Explore common models from a unified probabilistic perspective- Apply the Bayesian framework's flexibility for probabilistic thinkingWho this book is forIf you are a student, data scientist, researcher, or developer looking to get started with Bayesian data analysis and probabilistic programming, this book is for you. The book is introductory, so no previous statistical knowledge is required, although some experience in using Python and scientific libraries like NumPy is expected.Table of Contents- Thinking Probabilistically- Programming Probabilistically- Hierarchical Models- Modeling with Lines- Comparing Models- Modeling with Bambi- Mixture Models- Gaussian Processes- Bayesian Additive Regression Trees- Inference Engines- Where to Go Next