Foundations and Applications of Statistics

2018-04-04
Foundations and Applications of Statistics

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  • Author: Randall Pruim
  • Publisher: American Mathematical Soc.
  • ISBN: 1470428482
  • Category : Computers
  • Languages : en
  • Pages : 842

Foundations and Applications of Statistics simultaneously emphasizes both the foundational and the computational aspects of modern statistics. Engaging and accessible, this book is useful to undergraduate students with a wide range of backgrounds and career goals. The exposition immediately begins with statistics, presenting concepts and results from probability along the way. Hypothesis testing is introduced very early, and the motivation for several probability distributions comes from p-value computations. Pruim develops the students' practical statistical reasoning through explicit examples and through numerical and graphical summaries of data that allow intuitive inferences before introducing the formal machinery. The topics have been selected to reflect the current practice in statistics, where computation is an indispensible tool. In this vein, the statistical computing environment R is used throughout the text and is integral to the exposition. Attention is paid to developing students' mathematical and computational skills as well as their statistical reasoning. Linear models, such as regression and ANOVA, are treated with explicit reference to the underlying linear algebra, which is motivated geometrically. Foundations and Applications of Statistics discusses both the mathematical theory underlying statistics and practical applications that make it a powerful tool across disciplines. The book contains ample material for a two-semester course in undergraduate probability and statistics. A one-semester course based on the book will cover hypothesis testing and confidence intervals for the most common situations. In the second edition, the R code has been updated throughout to take advantage of new R packages and to illustrate better coding style. New sections have been added covering bootstrap methods, multinomial and multivariate normal distributions, the delta method, numerical methods for Bayesian inference, and nonlinear least squares. Also, the use of matrix algebra has been expanded, but remains optional, providing instructors with more options regarding the amount of linear algebra required.

Foundations of Statistics

1987-09-01
Foundations of Statistics

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  • Author: D.G. Rees
  • Publisher: CRC Press
  • ISBN: 9780412285608
  • Category : Mathematics
  • Languages : en
  • Pages : 564

This text provides a through, straightforward first course on basics statistics. Emphasizing the application of theory, it contains 200 fully worked examples and supplies exercises in each chapter-complete with hints and answers.

The Foundations of Statistics: A Simulation-based Approach

2010-11-11
The Foundations of Statistics: A Simulation-based Approach

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  • Author: Shravan Vasishth
  • Publisher: Springer Science & Business Media
  • ISBN: 3642163130
  • Category : Mathematics
  • Languages : en
  • Pages : 187

Statistics and hypothesis testing are routinely used in areas (such as linguistics) that are traditionally not mathematically intensive. In such fields, when faced with experimental data, many students and researchers tend to rely on commercial packages to carry out statistical data analysis, often without understanding the logic of the statistical tests they rely on. As a consequence, results are often misinterpreted, and users have difficulty in flexibly applying techniques relevant to their own research — they use whatever they happen to have learned. A simple solution is to teach the fundamental ideas of statistical hypothesis testing without using too much mathematics. This book provides a non-mathematical, simulation-based introduction to basic statistical concepts and encourages readers to try out the simulations themselves using the source code and data provided (the freely available programming language R is used throughout). Since the code presented in the text almost always requires the use of previously introduced programming constructs, diligent students also acquire basic programming abilities in R. The book is intended for advanced undergraduate and graduate students in any discipline, although the focus is on linguistics, psychology, and cognitive science. It is designed for self-instruction, but it can also be used as a textbook for a first course on statistics. Earlier versions of the book have been used in undergraduate and graduate courses in Europe and the US. ”Vasishth and Broe have written an attractive introduction to the foundations of statistics. It is concise, surprisingly comprehensive, self-contained and yet quite accessible. Highly recommended.” Harald Baayen, Professor of Linguistics, University of Alberta, Canada ”By using the text students not only learn to do the specific things outlined in the book, they also gain a skill set that empowers them to explore new areas that lie beyond the book’s coverage.” Colin Phillips, Professor of Linguistics, University of Maryland, USA

Foundations of Statistics for Data Scientists

2021-11-22
Foundations of Statistics for Data Scientists

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  • Author: Alan Agresti
  • Publisher: CRC Press
  • ISBN: 1000462919
  • Category : Business & Economics
  • Languages : en
  • Pages : 486

Foundations of Statistics for Data Scientists: With R and Python is designed as a textbook for a one- or two-term introduction to mathematical statistics for students training to become data scientists. It is an in-depth presentation of the topics in statistical science with which any data scientist should be familiar, including probability distributions, descriptive and inferential statistical methods, and linear modeling. The book assumes knowledge of basic calculus, so the presentation can focus on "why it works" as well as "how to do it." Compared to traditional "mathematical statistics" textbooks, however, the book has less emphasis on probability theory and more emphasis on using software to implement statistical methods and to conduct simulations to illustrate key concepts. All statistical analyses in the book use R software, with an appendix showing the same analyses with Python. The book also introduces modern topics that do not normally appear in mathematical statistics texts but are highly relevant for data scientists, such as Bayesian inference, generalized linear models for non-normal responses (e.g., logistic regression and Poisson loglinear models), and regularized model fitting. The nearly 500 exercises are grouped into "Data Analysis and Applications" and "Methods and Concepts." Appendices introduce R and Python and contain solutions for odd-numbered exercises. The book's website has expanded R, Python, and Matlab appendices and all data sets from the examples and exercises.

Statistical Foundations of Data Science

2020-09-21
Statistical Foundations of Data Science

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  • Author: Jianqing Fan
  • Publisher: CRC Press
  • ISBN: 0429527616
  • Category : Mathematics
  • Languages : en
  • Pages : 974

Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.

Statistical Foundations, Reasoning and Inference

2021-09-30
Statistical Foundations, Reasoning and Inference

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  • Author: Göran Kauermann
  • Publisher: Springer Nature
  • ISBN: 3030698270
  • Category : Mathematics
  • Languages : en
  • Pages : 361

This textbook provides a comprehensive introduction to statistical principles, concepts and methods that are essential in modern statistics and data science. The topics covered include likelihood-based inference, Bayesian statistics, regression, statistical tests and the quantification of uncertainty. Moreover, the book addresses statistical ideas that are useful in modern data analytics, including bootstrapping, modeling of multivariate distributions, missing data analysis, causality as well as principles of experimental design. The textbook includes sufficient material for a two-semester course and is intended for master’s students in data science, statistics and computer science with a rudimentary grasp of probability theory. It will also be useful for data science practitioners who want to strengthen their statistics skills.

Music Data Analysis

2016-11-17
Music Data Analysis

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  • Author: Claus Weihs
  • Publisher: CRC Press
  • ISBN: 1498719570
  • Category : Business & Economics
  • Languages : en
  • Pages : 694

This book provides a comprehensive overview of music data analysis, from introductory material to advanced concepts. It covers various applications including transcription and segmentation as well as chord and harmony, instrument and tempo recognition. It also discusses the implementation aspects of music data analysis such as architecture, user interface and hardware. It is ideal for use in university classes with an interest in music data analysis. It also could be used in computer science and statistics as well as musicology.

The Foundations of Statistics

2012-08-29
The Foundations of Statistics

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  • Author: Leonard J. Savage
  • Publisher: Courier Corporation
  • ISBN: 0486137104
  • Category : Mathematics
  • Languages : en
  • Pages : 341

Classic analysis of the foundations of statistics and development of personal probability, one of the greatest controversies in modern statistical thought. Revised edition. Calculus, probability, statistics, and Boolean algebra are recommended.

Statistics for High-Dimensional Data

2011-06-08
Statistics for High-Dimensional Data

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  • Author: Peter Bühlmann
  • Publisher: Springer Science & Business Media
  • ISBN: 364220192X
  • Category : Mathematics
  • Languages : en
  • Pages : 568

Modern statistics deals with large and complex data sets, and consequently with models containing a large number of parameters. This book presents a detailed account of recently developed approaches, including the Lasso and versions of it for various models, boosting methods, undirected graphical modeling, and procedures controlling false positive selections. A special characteristic of the book is that it contains comprehensive mathematical theory on high-dimensional statistics combined with methodology, algorithms and illustrations with real data examples. This in-depth approach highlights the methods’ great potential and practical applicability in a variety of settings. As such, it is a valuable resource for researchers, graduate students and experts in statistics, applied mathematics and computer science.

An Introduction to Statistical Learning

2023-08-01
An Introduction to Statistical Learning

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  • Author: Gareth James
  • Publisher: Springer Nature
  • ISBN: 3031387473
  • Category : Mathematics
  • Languages : en
  • Pages : 617

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, marketing, and 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. This book is targeted at statisticians and non-statisticians alike, who wish to use cutting-edge statistical learning techniques to analyze their data. Four of the authors co-wrote An Introduction to Statistical Learning, With Applications in R (ISLR), which has become a mainstay of undergraduate and graduate classrooms worldwide, as well as an important reference book for data scientists. One of the keys to its success was that each chapter contains a tutorial on implementing the analyses and methods presented in the R scientific computing environment. However, in recent years Python has become a popular language for data science, and there has been increasing demand for a Python-based alternative to ISLR. Hence, this book (ISLP) covers the same materials as ISLR but with labs implemented in Python. These labs will be useful both for Python novices, as well as experienced users.