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. |Introduction to Bayesian Data Analysis for Cognitive Science | Statistics
