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Statistical Thinking: a Simulation Approach to Modeling Uncertainty

Author : Andrew Zieffler

Publisher :

Page : 176 pages

File Size : 11,58 MB

Release : 2012-08-29

Category : Mathematical statistics

ISBN : 9780615691305

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Book Description

Learning statistics is sexy.Almost every person on earth will benefit from learning some foundational ideas of statistics. This is true because statistics forms the basis of our everyday world just as much as do science, technology, and politics. Google, Netflix, Twitter, Facebook, OKCupid, Match.com, Amazon, iTunes, and the Federal Government are just a handful of the companies and organizations that use statistics on a daily basis. Journalism, political science, biology, sociology, psychology, graphic design, economics, sports science, and dance are all disciplines that have made use of statistical methodology.The materials in this book will introduce you to the seminal ideas underlying the discipline of statistics. In addition, they have been designed with your learning in mind. As you engage in and use the skills, concepts and ideas introduced in the material, you will find yourself thinking about data and evidence in a different way.



Uncertainty

Author : William Briggs

Publisher : Springer

Page : 274 pages

File Size : 35,75 MB

Release : 2016-07-15

Category : Mathematics

ISBN : 3319397567

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Book Description

This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance." The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, such as out-of-the-box regression, cannot help in discovering cause. This new way of looking at uncertainty ties together disparate fields — probability, physics, biology, the “soft” sciences, computer science — because each aims at discovering cause (of effects). It broadens the understanding beyond frequentist and Bayesian methods to propose a Third Way of modeling.



Regression Modeling Strategies

Author : Frank E. Harrell

Publisher : Springer Science & Business Media

Page : 583 pages

File Size : 49,99 MB

Release : 2013-03-09

Category : Mathematics

ISBN : 147573462X

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Book Description

Many texts are excellent sources of knowledge about individual statistical tools, but the art of data analysis is about choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasizes problem solving strategies that address the many issues arising when developing multivariable models using real data and not standard textbook examples. It includes imputation methods for dealing with missing data effectively, methods for dealing with nonlinear relationships and for making the estimation of transformations a formal part of the modeling process, methods for dealing with "too many variables to analyze and not enough observations," and powerful model validation techniques based on the bootstrap. This text realistically deals with model uncertainty and its effects on inference to achieve "safe data mining".



Innovations in Multivariate Statistical Modeling

Author : Andriëtte Bekker

Publisher : Springer Nature

Page : 434 pages

File Size : 41,41 MB

Release : 2022-12-15

Category : Mathematics

ISBN : 3031139712

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Book Description

Multivariate statistical analysis has undergone a rich and varied evolution during the latter half of the 20th century. Academics and practitioners have produced much literature with diverse interests and with varying multidisciplinary knowledge on different topics within the multivariate domain. Due to multivariate algebra being of sustained interest and being a continuously developing field, its appeal breaches laterally across multiple disciplines to act as a catalyst for contemporary advances, with its core inferential genesis remaining in that of statistics. It is exactly this varied evolution caused by an influx in data production, diffusion, and understanding in scientific fields that has blurred many lines between disciplines. The cross-pollination between statistics and biology, engineering, medical science, computer science, and even art, has accelerated the vast amount of questions that statistical methodology has to answer and report on. These questions are often multivariate in nature, hoping to elucidate uncertainty on more than one aspect at the same time, and it is here where statistical thinking merges mathematical design with real life interpretation for understanding this uncertainty. Statistical advances benefit from these algebraic inventions and expansions in the multivariate paradigm. This contributed volume aims to usher novel research emanating from a multivariate statistical foundation into the spotlight, with particular significance in multidisciplinary settings. The overarching spirit of this volume is to highlight current trends, stimulate a focus on, and connect multidisciplinary dots from and within multivariate statistical analysis. Guided by these thoughts, a collection of research at the forefront of multivariate statistical thinking is presented here which has been authored by globally recognized subject matter experts.



International Handbook of Research in Statistics Education

Author : Dani Ben-Zvi

Publisher : Springer

Page : 523 pages

File Size : 19,91 MB

Release : 2017-12-08

Category : Education

ISBN : 3319661957

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Book Description

This handbook connects the practice of statistics to the teaching and learning of the subject with contributions from experts in several disciplines. Chapters present current challenges and methods of statistics education in the changing world for statistics and mathematics educators. Issues addressed include current and future challenges in professional development of teachers, use of technology tools, design of learning environments and appropriate student assessments. This handbook presents challenging and inspiring international research perspectives on the history and nature, current issues, and future directions of statistics education and statistics education research.



The Learning and Teaching of Statistics and Probability

Author : Luis Saldanha

Publisher : Taylor & Francis

Page : 165 pages

File Size : 38,83 MB

Release : 2023-12-01

Category : Education

ISBN : 1003805566

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Book Description

Filled with practical learning activities to adopt within your classroom, The Learning and Teaching of Statistics and Probability places reasoning about quantities and quantification at the core of learning and teaching statistics. A companion website to this book is also available at https://neilhatfield.github.io/IMPACT_Statistics/, allowing readers to access a directory of resources – data collections and web-based applets – used in some of the instructional activities featured within this book. Through its presentation of conceptual analyses and resources for teaching with statistical data, the book’s five chapters establish key concepts and foundational ideas in statistics and probability, emphasizing the development of learner understanding and coherence, for example: Individual cases and their attributes Data collections, sub-collections, and relevant operations to quantify their attributes Samples, population, and quantifying variation Types of processes, meanings of randomness, and probability as a measure of stochastic tendency Sampling distributions and statistical inference. This highly informative yet practical book is an indispensable resource for teachers of secondary school mathematics, mathematics subject leads, and mathematics and statistics educators within the wider field of education.



Statistical Inference as Severe Testing

Author : Deborah G. Mayo

Publisher : Cambridge University Press

Page : 503 pages

File Size : 25,43 MB

Release : 2018-09-20

Category : Mathematics

ISBN : 1108563309

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Book Description

Mounting failures of replication in social and biological sciences give a new urgency to critically appraising proposed reforms. This book pulls back the cover on disagreements between experts charged with restoring integrity to science. It denies two pervasive views of the role of probability in inference: to assign degrees of belief, and to control error rates in a long run. If statistical consumers are unaware of assumptions behind rival evidence reforms, they can't scrutinize the consequences that affect them (in personalized medicine, psychology, etc.). The book sets sail with a simple tool: if little has been done to rule out flaws in inferring a claim, then it has not passed a severe test. Many methods advocated by data experts do not stand up to severe scrutiny and are in tension with successful strategies for blocking or accounting for cherry picking and selective reporting. Through a series of excursions and exhibits, the philosophy and history of inductive inference come alive. Philosophical tools are put to work to solve problems about science and pseudoscience, induction and falsification.



The Science and Management of Uncertainty

Author : Bruce G. Marcot

Publisher : CRC Press

Page : 278 pages

File Size : 12,72 MB

Release : 2020-11-26

Category : Business & Economics

ISBN : 1000244512

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Book Description

Uncertainty can take many forms, can be represented in many ways, and can have important implications in decision-making and policy development. This book provides a rigorous scientific framework for dealing with uncertainty in real-world situations, and provides a comprehensive study of concepts, measurements, and applications of uncertainty in ecological modeling and natural resource management. The focus of this book is on the kinds and implications of uncertainty in environmental modeling and management, with practical guidelines and examples for successful modeling and risk analysis in the face of uncertain conditions and incomplete information. Provided is a clear classification of uncertainty; methods for measuring, modeling, and communicating uncertainty; practical guidelines for capturing and representing expert knowledge and judgment; explanations of the role of uncertainty in decision-making; a guideline to avoiding logical fallacies when dealing with uncertainty; and several example cases of real-world ecological modeling and risk analysis to illustrate the concepts and approaches. Case topics provide examples of structured decision-making, statistical modeling, and related topics. A summary provides practical next steps that the reader can take in analyzing and interpreting uncertainty in real-world situations. Also provided is a glossary and a suite of references.



Statistical Rethinking

Author : Richard McElreath

Publisher : CRC Press

Page : 488 pages

File Size : 16,64 MB

Release : 2018-01-03

Category : Mathematics

ISBN : 1315362619

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Book Description

Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation. By using complete R code examples throughout, this book provides a practical foundation for performing statistical inference. Designed for both PhD students and seasoned professionals in the natural and social sciences, it prepares them for more advanced or specialized statistical modeling. Web Resource The book is accompanied by an R package (rethinking) that is available on the author’s website and GitHub. The two core functions (map and map2stan) of this package allow a variety of statistical models to be constructed from standard model formulas.



Modeling and Simulation Fundamentals

Author : John A. Sokolowski

Publisher : John Wiley & Sons

Page : 468 pages

File Size : 12,31 MB

Release : 2010-04-19

Category : Mathematics

ISBN : 0470486740

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Book Description

An insightful presentation of the key concepts, paradigms, and applications of modeling and simulation Modeling and simulation has become an integral part of research and development across many fields of study, having evolved from a tool to a discipline in less than two decades. Modeling and Simulation Fundamentals offers a comprehensive and authoritative treatment of the topic and includes definitions, paradigms, and applications to equip readers with the skills needed to work successfully as developers and users of modeling and simulation. Featuring contributions written by leading experts in the field, the book's fluid presentation builds from topic to topic and provides the foundation and theoretical underpinnings of modeling and simulation. First, an introduction to the topic is presented, including related terminology, examples of model development, and various domains of modeling and simulation. Subsequent chapters develop the necessary mathematical background needed to understand modeling and simulation topics, model types, and the importance of visualization. In addition, Monte Carlo simulation, continuous simulation, and discrete event simulation are thoroughly discussed, all of which are significant to a complete understanding of modeling and simulation. The book also features chapters that outline sophisticated methodologies, verification and validation, and the importance of interoperability. A related FTP site features color representations of the book's numerous figures. Modeling and Simulation Fundamentals encompasses a comprehensive study of the discipline and is an excellent book for modeling and simulation courses at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners in the fields of computational statistics, engineering, and computer science who use statistical modeling techniques.