This book introduces Bayesian data analysis and Bayesian cognitive modeling to students and researchers in cognitive science (e.g., linguistics, psycholinguistics, psychology, computer science), with a particular focus on modeling data from planned experiments. The book relies on the probabilistic programming language Stan and the R package brms, which is a front-end to Stan. The book only assumes that the reader is familiar with the statistical programming language R, and has basic high school exposure to pre-calculus mathematics; some of the important mathematical constructs needed for the book are introduced in the first chapter.
Through this book, the reader will be able to develop a practical ability to apply Bayesian modeling within their own field. The book begins with an informal introduction to foundational topics such as probability theory, and univariate and bi-/multivariate discrete and continuous random variables. Then, the application of Bayes' rule for statistical inference is introduced with several simple analytical examples that require no computing software; the main insight here is that the posterior distribution of a parameter is a compromise between the prior and the likelihood functions. The book then gradually builds up the regression framework using the brms package in R, ultimately leading to hierarchical regression modeling (aka the linear mixed model). Along the way, there is detailed discussion about the topic of prior selection, and developing a well-defined workflow. Later chapters introduce the Stan programming language, and cover advanced topics using practical examples: contrast coding, model comparison using Bayes factors and cross-validation, hierarchical models and reparameterization, defining custom distributions, measurement error models and meta-analysis, and finally, some examples of cognitive models: multinomial processing trees, finite mixture models, and accumulator models. Additional chapters, appendices, and exercises are provided as online materials and can be accessed here: https://github.com/bnicenboim/bayescogsci.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Postgraduate and Professional
Illustrationen
151 s/w Abbildungen, 9 s/w Photographien bzw. Rasterbilder, 142 s/w Zeichnungen, 17 s/w Tabellen
17 Tables, black and white; 142 Line drawings, black and white; 9 Halftones, black and white; 151 Illustrations, black and white
Maße
Höhe: 179 mm
Breite: 256 mm
Dicke: 36 mm
Gewicht
ISBN-13
978-0-367-35933-1 (9780367359331)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Bruno Nicenboim is assistant professor in the department of Cognitive Science and Artificial Intelligence at Tilburg University in the Netherlands, working within the area of computational psycholinguistics.
Daniel J. Schad is a cognitive psychologist and is professor of Quantitative Methods at the HMU Health
and Medical University in Potsdam, Germany.
Shravan Vasishth is professor of psycholinguistics at the department of Linguistics at the University of Potsdam, Germany; he is a chartered statistician (Royal Statistical Society, UK).
Autor*in
Department of Cognitive Science and Artificial Intelligence, Tilburg University, Netherlands
Health and Medical University, Potsdam, Germany
Royal Statistical Society, UK and Department of Linguistics, University of Potsdam, Germany
Preface About the Authors I Foundational ideas 1 Introduction 2 Introduction to Bayesian data analysis II Regression models with brms 3 Computational Bayesian data analysis 4 Bayesian regression models 5 Bayesian hierarchical models 6 Contrast coding 7 Contrast coding with two predictor variables III Advanced models with Stan 8 Introduction to the probabilistic programming language Stan 9 Hierarchical models and reparameterization 10 Custom distributions in Stan IV Evidence synthesis and measurements with error 11 Meta-analysis and measurement error models V Model comparison 12 Introduction to model comparison 13 Bayes factors 14 Cross-validation VI Cognitive modeling with Stan 15 Introduction to cognitive modeling 16 Multinomial processing trees 17 Mixture models 18 A simple accumulator model to account for choice response time 19 In closing References
