Matematisk statistik

Business Statistics: Communicating with Numbers takes a comprehensive and contemporary approach that aims to bridge the gap between how statistics is taught and applied in the business world. This title not only prepares students in basic statistics but also gets them excited about further exploration of data analytics. The authors emphasize communicating with numbers rather than number crunching, through relatable case studies with relevant statistical methods and takeaways. This title incorporates timely examples from various fields, reinforces core features from previous editions, uses Excel and R to analyze data and solve problems, and includes new improvements, such as a revised chapter on data visualization, an exclusive chapter on logistic regression, and digital enhancements such as a big data capstone project with algorithmic exercises that span across multiple chapters.

Denna bok är en omarbetning av Kerstin Vännmans tidigare bok Matematisk statistik från 2002. Boken syftar till att träna det statistiska tänkandet så att man kan förstå och använda några ofta förekommande statistiska metoder. Den är uppbyggd kring ett stort antal exempel och nya begrepp introduceras och motiveras med hjälp av inledande exempel.I boken behandlas bland annat enkla sannolikhetsresonemang, några vanligt förekommande fördelningar, till exempel binomial-, Poisson-, normal- och exponential-fördelningen, samt olika läges- och spridningsmått. Vidare behandlas punktskattningar, konfidensintervall (även jämförande situationer) och test. Den största förändringen jämfört med den tidigare boken är att regressionsanalys (både enkel och multipel) och flerdimensionella stokastiska variabler behandlas i denna bok. I regressionsanalysen ligger fokus på tillämpning med hjälp av statistisk programvara och tolkning av resultat.Boken vänder sig i första hand till studenter inom utbildningarna för civil- och högskoleingenjörer, men den är även lämplig för annan högskoleutbildning eller för självstudier. Till varje kapitel finns ett stort antal övningsuppgifter med svar. Dessutom finns ett separat kapitel med blandade övningar av varierande svårighetsgrad.

'A necessary book for our times. But also just great fun' Saul Perlmutter, Nobel LaureateThe world is awash in bullshit, and we're drowning in it. Politicians are unconstrained by facts. Science is conducted by press release. Start-up culture elevates hype to high art. These days, calling bullshit is a noble act.Based on a popular course at the University of Washington, Calling Bullshit gives us the tools to see through the obfuscations, deliberate and careless, that dominate every realm of our lives. In this lively guide, biologist Carl Bergstrom and statistician Jevin West show that calling bullshit is crucial to a properly functioning social group, whether it be a circle of friends, a community of researchers, or the citizens of a nation. Through six rules of thumb, they help us recognize bullshit whenever and wherever we encounter it - even within ourselves - and explain it to a crystal-loving aunt or casually racist grandfather.

Grundläggande statistik för universitet och högskolor presenterar allmän statistisk teori på ett lättförståeligt och engagerande sätt. Författaren lägger stor vikt vid statistik som ett verktyg som kan användas för att lösa problem inom en rad olika områden, med realistiska exempel från arbetsliv och samhälle. Boken beskriver hur datorprogrammen Excel, SPSS, Minitab och R kan användas för statistiska beräkningar.Boken vänder sig till studenter som läser introduktionskurser i statistik inom de flesta studieområdena. Den kan också användas av personer som vill ha en bra och lättläst bok för att fräscha upp eller inhämta statistiska kunskaper genom självstudier.På studentlitteratur.se/43863 finns kompletterande digitalt material i form av övningsuppgifter, datamaterial och lärarmaterial.“Denna välskrivna lärobok erbjuder många intressanta och verklighetsnära exempel som hjälper studenterna att inte bara förstå den statistiska teorin, utan också att utveckla ett kritiskt och analytiskt statistiskt tänkande. Boken är särskilt lämplig som kurslitteratur i statistik på grundläggande nivå vid universitet och högskolor.”Niklas Karlsson, lektor i statistik vid Örebro universitet

Statistics: The Art and Science of Learning From Data, 5th Edition helps you understand what statistics is all about and learn the right questions to ask when analyzing data, instead of just memorizing procedures. It makes accessible the ideas that have turned statistics into a central science of modern life, without compromising essential material. Students often find this book enjoyable to read and stay engaged with the wide variety of real-world data in the examples and exercises. Based on the authors' belief that it's important for you to learn and analyze both quantitative and categorial data, this text pays greater attention to the analysis of proportions than many other introductory statistics texts.

Key features include:

Greater attention to the analysis of proportions compared to other introductory statistics texts. Introduction to key concepts, presenting the categorical data first, and quantitative data after. A wide variety of real-world data in the examples and exercises New sections and updated content will enhance your learning and understanding.

Pearson MyLab® Students, if Pearson Pearson MyLab Statistics is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. Pearson MyLab Statistics should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

 

Neil J. Salkind’s best-selling Statistics for People Who (Think They) Hate Statistics has been helping ease student anxiety around an often intimidating subject since it first published in 2000. Now the bestselling SPSS and Excel versions are joined by a first edition of the text for use with the R software. New co-author Leslie A. Shaw carries forward Neil’s signature humorous, personable, and informative approach. The text guides students through various statistical procedures, beginning with descriptive statistics, correlation, and graphical representation of data, and ending with inferential techniques and analysis of variance.

Features and benefits:

·         Lots of support for getting started with R: Included are two introductory chapters on R and on R Studio, plus an appendix on other R packages and resource sites.

·         Step-by-step demonstrations of each statistical procedure in R: The authors show how to import the dataset, enter the syntax to run the test, and understand the output.

·         Additional resources make it easy to transition to this text, and to R:  Code and datasets are available on an accompanying website, which also includes screencast R tutorial videos for students, and PowerPoint slides and additional test questions for instructors.

Kan statistik verkligen vara intressant och lätt att förstå? Svaret är ja! Denna bok bryter ned de komplexa principerna för statistisk analys och gör dem tillgängliga för alla. Så oavsett om du är student, forskare eller bara nyfiken på statistik, kommer du att finna värdefull vägledning här.Kan jag lita på statistiken? Hur stor är den statistiska felmarginalen? Är förändringen statistiskt säkerställd? Vad innebär statistisk signifikans? Svaren på dessa och många andra frågor finns i den här boken. Med praktiska tillämpningar och utan krånglig matematik förklaras grunderna för statistisk beskrivning, kritisk granskning och statistisk analys. Det finns många exempel med fullständiga lösningar och övningsuppgifter med utförliga svar i boken. Därför bör den fungera bra även för den som vill lära sig statistik på egen hand. I slutet på varje kapitel finns avsnittet Med datorns hjälp. Där visas hur man med statistikprogrammet SPSS kan låta datorn göra det siffermässiga grovarbetet. Statistik upplevs av många som svårt och tråkigt. Med denna bok visar författarna ännu en gång att statistik både kan vara lätt och roligt.

Shortlisted for the William Hill Sports Book of the Year Award 2022 Football has always measured success by what you win, but only in the last twenty years have clubs started to think about how you win. Data has now suffused almost every aspect of how football is played, coached, scouted and consumed. But it’s not the algorithms or new metrics that have made this change, it’s the people behind them.This is the story of modern football’s great data revolution and the group of curious, entrepreneurial personalities who zealously believed in its potential to transform the game. Central to this cast is Chris Anderson, an academic with no experience in football, who saw data as an opportunity to fundamentally change a sport that did not think it could be changed. His aim: to infiltrate the strange, insular world of professional football by establishing a club whose entire DNA could be built around data.Expected Goals charts his remarkable journey into the heart of the modern game and reveals how clubs across the world, from Liverpool to Leipzig and Brentford to Bayern Munich, began to see how data could help them unearth new players, define radical tactics and plot their path to glory.

Engineers are expected to design structures and machines that can operate in challenging and volatile environments, while allowing for variation in materials and noise in measurements and signals. Statistics in Engineering, Second Edition: With Examples in MATLAB and R covers the fundamentals of probability and statistics and explains how to use these basic techniques to estimate and model random variation in the context of engineering analysis and design in all types of environments.The first eight chapters cover probability and probability distributions, graphical displays of data and descriptive statistics, combinations of random variables and propagation of error, statistical inference, bivariate distributions and correlation, linear regression on a single predictor variable, and the measurement error model. This leads to chapters including multiple regression; comparisons of several means and split-plot designs together with analysis of variance; probability models; and sampling strategies.Key features: All examples based on work in industry, consulting to industry, and research for industry Examples and case studies include all engineering disciplinesEmphasis on probabilistic modeling including decision trees, Markov chains and processes, and structure functionsIntuitive explanations are followed by succinct mathematical justificationsEmphasis on random number generation that is used for stochastic simulations of engineering systems, demonstration of key concepts, and implementation of bootstrap methods for inferenceUse of MATLAB and the open source software R, both of which have an extensive range of statistical functions for standard analyses and also enable programing of specific applicationsUse of multiple regression for times series models and analysis of factorial and central composite designs Inclusion of topics such as Weibull analysis of failure times and split-plot designs that are commonly used in industry but are not usually included in introductory textbooksExperiments designed to show fundamental concepts that have been tested with large classes working in small groupsWebsite with additional materials that is regularly updated

Shortlisted for the William Hill Sports Book of the Year Award 2022 Football has always measured success by what you win, but only in the last twenty years have clubs started to think about how you win. Data has now suffused almost every aspect of how football is played, coached, scouted and consumed. But it’s not the algorithms or new metrics that have made this change, it’s the people behind them.This is the story of modern football’s great data revolution and the group of curious, entrepreneurial personalities who zealously believed in its potential to transform the game. Central to this cast is Chris Anderson, an academic with no experience in football, who saw data as an opportunity to fundamentally change a sport that did not think it could be changed. His aim: to infiltrate the strange, insular world of professional football by establishing a club whose entire DNA could be built around data.Expected Goals charts his remarkable journey into the heart of the modern game and reveals how clubs across the world, from Liverpool to Leipzig and Brentford to Bayern Munich, began to see how data could help them unearth new players, define radical tactics and plot their path to glory.

'A great introduction to a crucial topic' Bill Gates'Perhaps the most popular book on statistics ever published ... It's a marvel ... gave me a peek behind the curtain of statistical manipulation, showing me how the swindling was done so that I would not be fooled again' Tim HarfordIn 1954, Darrell Huff decided enough was enough. Fed up with politicians, advertisers and journalists using statistics to sensationalise, inflate, confuse, oversimplify and - on occasion - downright lie, he decided to shed light on their ill-informed and sneaky ways. How to Lie with Statistics is the result - the definitive and hilarious primer in the ways statistics are used to deceive.With over one and half million copies sold around the world, it has delighted generations of readers with its cheeky takes on the ins and outs of samples, averages, errors, graphs and indexes. And in the modern world of big data and misinformation, Huff remains the perfect guide through the maze of facts and figures that are designed to make us believe anything.'A hilarious exploration of mathematical mendacity.... Every time you pick it up, what happens? Bang goes another illusion!' The New York Times'A pleasantly subversive little book guaranteed to undermine your faith in the almighty statistic' Atlantic

Vad är kvantitativa metoder? Hur kan de användas? Hur genomför man och planerar en undersökning? Hur kan och bör man tolka olika resultat och vilka osäkerhetsfaktorer finns det att ta hänsyn till vid resultattolkningar? Hur hjälper oss slumpen i att förstå och tolka rimligheten i olika resultat?Grunderna i statistisk dataanalys går igenom frågorna ovan och syftar till att ge kunskap om hur man planerar och genomför enklare undersökningar och hur man ska förhålla sig kritiskt till avancerade studier och forskningsresultat.Boken avslutas med ett kapitel om matematik för den som behöver repetera grundläggande kunskaper. Alla data som används i bokens olika exempel finns samlade i ett Excelark som kan hämtas från bokens webbplats. På så sätt kan läsaren upprepa det som görs i boken och även experimentera ytterligare.Boken riktar sig till blivande sjuksköterskor, fysio- och arbetsterapeuter, tandhygienister samt folkhälsovetare och även till övriga hälso- och sjukvårdsutbildningar.

‘Probably the UK’s greatest living statistician’ TelegraphFrom the UK’s ‘statistical national treasure’, a clever and data-driven guide to how we can live with risk and uncertaintyWe live in a world where uncertainty is inevitable. How should we deal with what we don’t know? And what role do chance, luck and coincidence play in our lives?David Spiegelhalter has spent his career dissecting data in order to understand risks and assess the chances of what might happen in the future. In The Art of Uncertainty, he gives readers a window onto how we can all do this better.In engaging, crystal-clear prose, he takes us through the principles of probability, showing how it can help us think more analytically about everything from medical advice to pandemics and climate change forecasts, and explores how we can update our beliefs about the future in the face of constantly changing experience. Along the way, he explains why roughly 40% of football results come down to luck rather than talent, how the National Risk Register assesses near-term risks to the United Kingdom, and why we can be so confident that two properly shuffled packs of cards have never, ever been in the exact same order.Drawing on a wide range of captivating real-world examples, this is an essential guide to navigating uncertainty while also having the humility to admit what we do not know

Once considered tedious, the field of statistics is rapidly evolving into a discipline Hal Varian, chief economist at Google, has actually called "sexy." From batting averages and political polls to game shows and medical research, the real-world application of statistics continues to grow by leaps and bounds. How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more.For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, deep learning, survival analysis, multiple testing, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform.Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.This Second Edition features new chapters on deep learning, survival analysis, and multiple testing, as well as expanded treatments of naïve Bayes, generalized linear models, Bayesian additive regression trees, and matrix completion. R code has been updated throughout to ensure compatibility.

Statistikämnet behandlar metoder för att skapa kunskap genom att göra observationer. Att tolka och förstå statistik är en viktig vetenskaplig färdighet men också många gånger en förutsättning för ett kritiskt förhållningssätt i vardagen. Statistikens grunder syftar till att skapa förståelse för hur statistiska metoder används för att generera kunskap och hur dessa metoder fungerar respektive inte fungerar. Statistikens grunder tar avstamp i vetenskapsteori och vetenskapens grundbegrepp och sätter på detta sätt in statistikämnet i sitt vetenskapliga sammanhang. Boken går därefter ingående igenom ämnets grunder från sannolikhetsteori via empiriska undersökningar och deskription till statistisk inferens. Detta ger en uppsättning grundläggande verktyg som krävs för att utföra statistiska analyser och för att kritiskt granska tidigare analyser. Statistikens grunder lyfter också fram varför statistiska metoder kan användas i vissa situationer men inte i andra. I denna andra upplaga har en utökad och fördjupad diskussion om urvalsundersökningar, variansanalys och regressionsanalys införts. Boken är avsedd som litteratur på en introduktionskurs i statistik, men kan även användas som en metodbok för studerande på alla nivåer, från grundkurs till forskarnivå, i ämnesområden där statistiska metoder kommer till användning.

Dig deep to discover the truth about numbers and statistics in the mediaWrong Number: How to Extract Truth From a Blizzard of Quantitative Disinformation shows readers how to diagnose statistical errors in journal articles and media accounts of prominent public issues. In addition to the mistakes or tricks with numbers other people use to lose the truth, this book also offers more positive material, showing how to use numbers to find truth.Written by Aaron Brown, prominent media figure, former professor, sports bettor, and poker player, and host of the popular ReasonTV series Wrong Number, this book answers questions including: Did California’s minimum wage hike really create more jobs?Do studies show that weed causes strokes and heart attacks?Are poor geniuses being shut out of science?What is the real health risk of vaping?Does gun control work?Wrong Number: How to Extract Truth From a Blizzard of Quantitative Disinformation is an entertaining and eye-opening read for students in quantitative programs of study, along with all individuals curious as to whether or not they’re being told the truth from their favorite media organizations.

Leonard Mlodinow's The Drunkard's Walk: How Randomness Rules Our Lives is an exhilarating, eye-opening guide to understanding our random world.Randomness and uncertainty surround everything we do. So why are we so bad at understanding them? The same tools that help us understand the random paths of molecules can be applied to the randomness that governs so many aspects of our everyday lives, from winning the lottery to road safety, and reveals the truth about the success of sporting heroes and film stars, and even how to make sense of a blood test.The Drunkard's Walk reveals the psychological illusions that prevent us understanding everything from stock-picking to wine-tasting - read it, or risk becoming another victim of chance.'A wonderfully readable guide to how the mathematical laws of randomness affect our lives' Stephen Hawking, author of A Brief History of Time

This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.

'A statistical national treasure' Jeremy Vine, BBC Radio 2'Required reading for all politicians, journalists, medics and anyone who tries to influence people (or is influenced) by statistics. A tour de force' Popular ScienceDo busier hospitals have higher survival rates? How many trees are there on the planet? Why do old men have big ears? David Spiegelhalter reveals the answers to these and many other questions - questions that can only be addressed using statistical science.Statistics has played a leading role in our scientific understanding of the world for centuries, yet we are all familiar with the way statistical claims can be sensationalised, particularly in the media. In the age of big data, as data science becomes established as a discipline, a basic grasp of statistical literacy is more important than ever. In The Art of Statistics, David Spiegelhalter guides the reader through the essential principles we need in order to derive knowledge from data. Drawing on real world problems to introduce conceptual issues, he shows us how statistics can help us determine the luckiest passenger on the Titanic, whether serial killer Harold Shipman could have been caught earlier, and if screening for ovarian cancer is beneficial. 'Shines a light on how we can use the ever-growing deluge of data to improve our understanding of the world' Nature

In their bestselling title MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors' use of practical applications and excellent exercises helps you discover the nature of statistics and understand its essential role in scientific research.With the addition of contributor Brendan Ames, MATHEMATICAL STATISTICS WITH APPLICATIONS now includes an enhanced eTextbook. Simulation activities using interactive applets and R embedded within the MindTap Reader help students visualize statistical concepts, and an appendix introducing students to statistical data analysis using R can be found at the end of the eTextbook.

This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. The main mode of presentation is via code examples with liberal commenting of the code and the output, from the computational as well as the statistical viewpoint. Brief sections introduce the statistical methods before they are used. A supplementary R package can be downloaded and contains the data sets. All examples are directly runnable and all graphics in the text are generated from the examples. The statistical methodology covered includes statistical standard distributions, one- and two-sample tests with continuous data, regression analysis, one- and two-way analysis of variance, regression analysis, analysis of tabular data, and sample size calculations. In addition, the last four chapters contain introductions to multiple linear regression analysis, linear models in general, logistic regression, and survival analysis.

Expert coverage of the design and implementation of state estimation algorithms for tracking and navigationEstimation with Applications to Tracking and Navigation treats the estimation of various quantities from inherently inaccurate remote observations. It explains state estimator design using a balanced combination of linear systems, probability, and statistics.The authors provide a review of the necessary background mathematical techniques and offer an overview of the basic concepts in estimation. They then provide detailed treatments of all the major issues in estimation with a focus on applying these techniques to real systems. Other features include:* Problems that apply theoretical material to real-world applications* In-depth coverage of the Interacting Multiple Model (IMM) estimator* Companion DynaEst(TM) software for MATLAB(TM) implementation of Kalman filters and IMM estimators* Design guidelines for tracking filtersSuitable for graduate engineering students and engineers working in remote sensors and tracking, Estimation with Applications to Tracking and Navigation provides expert coverage of this important area.

For junior/senior undergraduates taking probability and statistics as applied to engineering, science, or computer science.

This classic text provides a rigorous introduction to basic probability theory and statistical inference, with a unique balance between theory and methodology. Interesting, relevant applications use real data from actual studies, showing how the concepts and methods can be used to solve problems in the field. This revision focuses on improved clarity and deeper understanding.

Winner of the 2023 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA)Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds your knowledge of and confidence in making inferences from data. Reflecting the need for scripting in today's model-based statistics, the book pushes you to perform step-by-step calculations that are usually automated. This unique computational approach ensures that you understand enough of the details to make reasonable choices and interpretations in your own modeling work.The text presents causal inference and generalized linear multilevel models from a simple Bayesian perspective that builds on information theory and maximum entropy. The core material ranges from the basics of regression to advanced multilevel models. It also presents measurement error, missing data, and Gaussian process models for spatial and phylogenetic confounding.The second edition emphasizes the directed acyclic graph (DAG) approach to causal inference, integrating DAGs into many examples. The new edition also contains new material on the design of prior distributions, splines, ordered categorical predictors, social relations models, cross-validation, importance sampling, instrumental variables, and Hamiltonian Monte Carlo. It ends with an entirely new chapter that goes beyond generalized linear modeling, showing how domain-specific scientific models can be built into statistical analyses.FeaturesIntegrates working code into the main text. Illustrates concepts through worked data analysis examples. Emphasizes understanding assumptions and how assumptions are reflected in code. Offers more detailed explanations of the mathematics in optional sections. Presents examples of using the dagitty R package to analyze causal graphs. Provides the rethinking R package on the author's website and on GitHub.

This book gives a thorough introduction to mathematical statistics. The text is unique as an introductory text, mainly by the use of the Riemann-Stieltjes integral. This enables a unified treatment of basic concepts in probability and inference theory, in a mathematically rigorous manner, without the use of measure theory. The approach differentiates this book from other introductory texts, where one does not give a unified approach to basic concepts, as well as from advanced texts, where one does give a unified approach relying on advanced mathematics. The treatment of probability theory differs from comparable books in that one discusses basic concepts rigorously but without the use of Lebesgue integration. Thereby it allows one to concentrate on the basic concepts of mathematical statistics, without sacrifice of mathematical stringency. The approach also enables a concise definition of the plug-in estimator in inference theory. Arguably, the plug-in estimator is the most natural and intuitive estimator possible. The introduction of it is however mathematically advanced, and typically covered in PhD level texts. Using the Riemann-Stieltjes integral the introduction of it becomes elementary. The book is intended for students at the Faculty of Science and Faculty of Engineering that have taken a full year of basic mathematics courses, including real analysis and linear algebra.

This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation the text begins with a survey of classical probability theory and with an introduction into the foundations of quantum mechanics with particular emphasis on its statistical interpretation. The fundamentals of density matrix theory, quantum Markov processes and dynamical semigroups are developed. The most important master equations used in quantum optics and in the theory of quantum Brownian motion are applied to the study of many examples. Special attention is paid to the theory of environment induced decoherence, its role in the dynamical description of the measurement process and to the experimental observation of decohering Schrodinger cat states.The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics, such as Levy statistics in the laser cooling of atoms, and the damped Jaynes-Cummings model. The basic features of the non-Markovian quantum behaviour of open systems are examined on the basis of projection operator techniques. In addition, the book expounds the relativistic theory of quantum measurements and discusses several examples from a unified perspective, e.g. non-local measurements and quantum teleportation. Influence functional and super-operator techniques are employed to study the density matrix theory in quantum electrodynamics and applications to the destruction of quantum coherence are presented.The text addresses graduate students and lecturers in physics and applied mathematics, as well as researchers with interests in fundamental questions in quantum mechanics and its applications. Many analytical methods and computer simulation techniques are developed and illustrated with the help of numerous specific examples. Only a basic understanding of quantum mechanics and of elementary concepts of probability theory is assumed.