Название: Statistics by Simulation: A Synthetic Data Approach
Автор: Carsten F. Dormann, Aaron M. Ellison
Издательство: Princeton University Press
Год: 2025
Страниц: 457
Язык: английский
Формат: pdf (true)
Размер: 12.9 MB

An accessible guide to understanding statistics using simulations, with examples from a range of scientific disciplines.

Real-world challenges such as small sample sizes, skewed distributions of data, biased sampling designs, and more predictors than data points are pushing the limits of classical statistical analysis. This textbook provides a new tool for the statistical toolkit: data simulations. It shows that using simulation and data-generating models is an excellent way to validate statistical reasoning and to augment study design and statistical analysis with planning and visualization. Although data simulations are not new to professional statisticians, Statistics by Simulation makes the approach accessible to a broader audience, with examples from many fields. It introduces the reasoning behind data simulation and then shows how to apply it in planning experiments or observational studies, developing analytical workflows, deploying model diagnostics, and developing new indices and statistical methods.

• Covers all steps of statistical practice, from planning projects to post-hoc analysis and model checking
• Provides examples from disciplines including sociology, psychology, ecology, economics, physics, and medicine
• Includes R code for all examples, with data and code freely available online
• Offers bullet-point outlines and summaries of each chapter
• Minimizes the use of jargon and requires only basic statistical background and skills

The book is organised in five parts. First, we introduce the reasoning behind simulations using familiar and practical examples (Part I). We then proceed to show how to use simulations to plan experiments or observational studies and preregister them (Part II); how to use simulations to explore the consequences of violating the assumptions of standard statistical models, differentiate myths from reality in common statistical guidelines and rules-of-thumb, and develop analytical workflows (Part III); and how to take advantage of simulations to explore model fits and assess them with model diagnostics while not drowning in the swamp of retrospective power analysis and post hoc justifications for “non-signficant” results (Part IV). Finally, in Part V, we illustrate the importance of using simulations for synthesising and modelling data across many studies using classical metaanalysis and the emerging and powerful federated networks of data analysis for integrating, analysing, and synthesising sensitive, protected, or otherwise siloed data. We conclude Part V with a discussion of the crucial role of simulation in the development of new statistical indices, metrics, and methods, and the associated emerging standards that require simulation as a condition for publishing such methods in ecology and medicine.

All of our examples are accompanied by reproducible code (in the R programming language) that can be modified easily for related problems or translated into comparable software or programming languages such as Python or Julia using large language models such as Llama, StarCoder, or BLOOM. Detailed footnotes and extensive bibliographies in each chapter provide additional pointers to similar problems and comparable simulations in a range of fields. The 12 chapters of the book could be comfortably covered in a semester-long, discipline-specific course in applied statistics for (post)graduate students or advanced undergraduates.