Nicenboim B. Introduction to Bayesian Data Analysis for Cognitive Science 2026

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Nicenboim B. Introduction to Bayesian Data Analysis for Cognitive Science 2026

Textbook in PDF format 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 in GitHub. Why read this book, and what is its target audience? A commonly held belief in psychology, psycholinguistics, and other areas is that statistical data analysis is secondary to the science and should be quick and easy. For example, a senior mathematical psychologist once told the last author of this book: “if you need to run anything more complicated than a paired t-test, you are asking the wrong question.” We take a different perspective here: the science and the statistical modeling are one unitary thing. The statistical model should represent some reasonable approximation of the latent cognitive processes that are assumed to be in play. The target audience for this book is students and researchers who want to treat statistics as an equal partner in their scientific work. We expect that the reader is willing to take the time to both understand and run the computational analyses. Any rigorous introduction to Bayesian data analysis requires at least a passive knowledge of probability theory, calculus, and linear algebra. However, we do not require that the reader has this background when they start the book. Instead, the relevant ideas are introduced informally and just in time, as soon as they are needed. The reader is never required to have an active ability to solve probability problems, to solve integrals or compute derivatives, or to carry out matrix computations (such as inverting matrices) by hand. There are a few places where the discussion becomes technical and requires some knowledge of calculus or related topics