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

A comprehensive introduction to sampling-based methods in statistical computing The use of computers in mathematics and statistics has opened up a wide range of techniques for studying otherwise intractable problems. Sampling-based simulation techniques are now an invaluable tool for exploring statistical models. This book gives a comprehensive introduction to the exciting area of sampling-based methods. An Introduction to Statistical Computing introduces the classical topics of random number generation and Monte Carlo methods. It also includes some advanced methods such as the reversible jump Markov chain Monte Carlo algorithm and modern methods such as approximate Bayesian computation and multilevel Monte Carlo techniques An Introduction to Statistical Computing: Fully covers the traditional topics of statistical computing. Discusses both practical aspects and the theoretical background. Includes a chapter about continuous-time models. Illustrates all methods using examples and exercises. Provides answers to the exercises (using the statistical computing environment R); the corresponding source code is available online. Includes an introduction to programming in R. This book is mostly self-contained; the only prerequisites are basic knowledge of probability up to the law of large numbers. Careful presentation and examples make this book accessible to a wide range of students and suitable for self-study or as the basis of a taught course.

The OpenIntro project was founded in 2009 to improve the quality and availability of education by producing exceptional books and teaching tools that are free to use and easy to modify. We feature real data whenever possible, and files for the entire textbook are freely available at openintro.org. Visit our website, openintro.org. We provide free videos, statistical software labs, lecture slides, course management tools, and many other helpful resources.

This book brings together expert researchers engaged in Monte-Carlo simulation-based statistical modeling, offering them a forum to present and discuss recent issues in methodological development as well as public health applications. It is divided into three parts, with the first providing an overview of Monte-Carlo techniques, the second focusing on missing data Monte-Carlo methods, and the third addressing Bayesian and general statistical modeling using Monte-Carlo simulations. The data and computer programs used here will also be made publicly available, allowing readers to replicate the model development and data analysis presented in each chapter, and to readily apply them in their own research. Featuring highly topical content, the book has the potential to impact model development and data analyses across a wide spectrum of fields, and to spark further research in this direction.

This textbook may be downloaded as a free PDF on the project's website, and the paperback is sold royalty-free. OpenIntro develops free textbooks and course resources for introductory statistics that exceeds the quality standards of traditional textbooks and resources, and that maximizes accessibility options for the typical student. The approach taken in this textbooks differs from OpenIntro Statistics in its introduction to inference. The foundations for inference are provided using randomization and simulation methods. Once a solid foundation is formed, a transition is made to traditional approaches, where the normal and t distributions are used for hypothesis testing and the construction of confidence intervals.

Harness actionable insights from your data with computational statistics and simulations using R About This Book Learn five different simulation techniques (Monte Carlo, Discrete Event Simulation, System Dynamics, Agent-Based Modeling, and Resampling) in-depth using real-world case studies A unique book that teaches you the essential and fundamental concepts in statistical modeling and simulation Who This Book Is For This book is for users who are familiar with computational methods. If you want to learn about the advanced features of R, including the computer-intense Monte-Carlo methods as well as computational tools for statistical simulation, then this book is for you. Good knowledge of R programming is assumed/required. What You Will Learn The book aims to explore advanced R features to simulate data to extract insights from your data. Get to know the advanced features of R including high-performance computing and advanced data manipulation See random number simulation used to simulate distributions, data sets, and populations Simulate close-to-reality populations as the basis for agent-based micro-, model- and design-based simulations Applications to design statistical solutions with R for solving scientific and real world problems Comprehensive coverage of several R statistical packages like boot, simPop, VIM, data.table, dplyr, parallel, StatDA, simecol, simecolModels, deSolve and many more. In Detail Data Science with R aims to teach you how to begin performing data science tasks by taking advantage of Rs powerful ecosystem of packages. R being the most widely used programming language when used with data science can be a powerful combination to solve complexities involved with varied data sets in the real world. The book will provide a computational and methodological framework for statistical simulation to the users. Through this book, you will get in grips with the software environment R. After getting to know the background of popular methods in the area of computational statistics, you will see some applications in R to better understand the methods as well as gaining experience of working with real-world data and real-world problems. This book helps uncover the large-scale patterns in complex systems where interdependencies and variation are critical. An effective simulation is driven by data generating processes that accurately reflect real physical populations. You will learn how to plan and structure a simulation project to aid in the decision-making process as well as the presentation of results. By the end of this book, you reader will get in touch with the software environment R. After getting background on popular methods in the area, you will see applications in R to better understand the methods as well as to gain experience when working on real-world data and real-world problems. Style and approach This book takes a practical, hands-on approach to explain the statistical computing methods, gives advice on the usage of these methods, and provides computational tools to help you solve common problems in statistical simulation and computer-intense methods.

Although power method polynomials based on the standard normal distributions have been used in many different contexts for the past 30 years, it was not until recently that the probability density function (pdf) and cumulative distribution function (cdf) were derived and made available. Focusing on both univariate and multivariate nonnormal data ge