Preface

This is the second volume in a graduate sequence on statistical computing for biostatistics. The first volume, Statistical Computing in the Age of AI, treats the foundational material that a one-quarter graduate course typically covers: programming in R, numerical linear algebra, optimization, simulation, the bootstrap, the standard statistical models, and reproducibility infrastructure. The present volume begins where the first concludes and takes up the topics that a one-year graduate sequence builds toward.

We assume of the reader one year of graduate biostatistics study. In particular we assume the linear algebra and probability of a typical first-year sequence, fluency in R at the level of R for Data Science and Advanced R, a working knowledge of generalized linear and mixed-effects models, and a practical literacy in the bootstrap and in simulation. The material of the introductory SCAI volume is therefore prerequisite, and we do not recapitulate it here.

What this book covers

The thirteen chapters are organized in five parts.

  1. Numerical foundations: computer arithmetic and conditioning; numerical linear algebra in depth.
  2. Optimization and estimation: advanced optimization; the EM algorithm and its extensions.
  3. Monte Carlo and Bayesian computation: Monte Carlo methods in depth; MCMC in depth; modern Bayesian computation with Stan, variational inference, and model comparison.
  4. Scaling and modeling: high-performance and distributed computing; high-dimensional and sparse methods; machine learning for biostatistics.
  5. Software engineering and communication: software engineering for statisticians; reproducible computational environments; advanced interactive visualization.

We did not arrive at this list by intuition. It was constructed by surveying advanced statistical-computing syllabi from a dozen major US biostatistics programs, a survey documented in docs/syllabi-survey.md, and by adopting those topics that appeared in three or more of them. The result is, we believe, the mainstream curriculum for an advanced graduate computing course, with the addition of an explicit treatment of AI collaboration in every chapter.

What this book does not cover

We have deliberately omitted several topics that are usually taught in dedicated methods courses elsewhere in a biostatistics curriculum:

  • Causal inference (propensity scores, instrumental variables, mediation, marginal structural models).
  • Longitudinal data analysis beyond the GLMM material in SCAI.
  • Missing-data methods in depth (multiple imputation, MNAR sensitivity analysis, full-information maximum likelihood).
  • Meta-analysis, both network and individual-patient-data.

Each of these is, properly, a course in its own right; to include them here would make the book unusual relative to its peers and would dilute the computing focus. Where such topics arise we provide pointers to the standard references.

Age-of-AI framing

Every chapter carries two named sections that earn the subtitle ‘in the Age of AI’. The first, The statistician’s contribution, is placed early: it sets out the judgments at the center of the chapter that no large language model can make on the reader’s behalf. The second, Collaborating with an LLM on the topic at hand, comes at the end and offers specific prompts, each paired with what to watch for and how to verify the result. Together they treat AI assistance as an amplifier to be used with discipline rather than as a replacement for the statistical judgment the rest of the curriculum exists to build.

Where does the division of labor between the statistician and the model matter most? In the advanced material, we would suggest, rather than the foundational. A foundational chapter can survive a careless prompt; an advanced one cannot. We apply the framework throughout.

How to read this book

Each content chapter follows the same structure: Learning objectives, Orientation, The statistician’s contribution, the content sections (with collapsible Check-your-understanding callouts at natural pauses), Collaborating with an LLM, Exercises, and Further reading.

The chapters may be read in order or out of it. Where a genuine chain of dependencies exists, for example chapter 6 building on chapter 5 and chapter 7 on chapter 6, we note it in the relevant Orientation section.

Acknowledgments

A peer survey of US biostatistics MS programs shaped the chapter list. The authors of R for Data Science, Advanced R, R Packages, Bayesian Data Analysis, and Statistical Rethinking established conventions that this book inherits, and Mastering Shiny and ggplot2 informed both the visual-design decisions and the chapter-template layout.