1  Introduction

1.1 What this book is

This is a graduate textbook in advanced statistical computing for biostatistics, intended as the second volume in a two-book sequence. The introductory volume, Statistical Computing in the Age of AI, covers programming, numerical linear algebra, optimization, simulation, the bootstrap, the standard statistical models, and reproducibility infrastructure at a one-quarter graduate pace. The present volume begins where that one leaves off.

1.2 What ‘advanced’ means here

The word ‘advanced’ carries three meanings in this book, in increasing strength.

The first is a deeper treatment of foundational topics. Chapters 1 and 2, on numerical stability and numerical linear algebra, revisit material the introductory volume touches but does not treat in depth. Floating-point arithmetic, condition numbers, sparse and iterative solvers, and BLAS-level performance are the load-bearing fundamentals for everything that follows, and an advanced book that omits them is, we would argue, missing a layer.

The second is topics that exceed introductory scope. Chapters 3 through 7, on advanced optimization, the EM algorithm and its extensions, Monte Carlo in depth, MCMC in depth, and modern Bayesian computation, extend the introductory treatment of each into the territory needed for current methodological research and for applied practice with modern tools.

The third is topics that did not appear in the introductory volume at all. Chapters 8 through 13, on high-performance computing, high-dimensional methods, machine learning, software engineering for statisticians, reproducible computational environments, and advanced interactive visualization, cover ground the introductory volume deliberately set aside. Each is the kind of topic a practicing biostatistician meets mid-career, and that graduate training ought to prepare them for.

1.3 What ‘in the Age of AI’ commits the book to

The subtitle is a structural commitment and not decoration. Every chapter carries two named sections that exercise it.

The first, The statistician’s contribution, is placed early: it is an explicit articulation of the judgments at the center of the chapter that no large language model can make on the reader’s behalf. Advanced material is exactly where the human-LLM division of labor matters most. A careless prompt in an introductory bootstrap chapter produces a bug that a re-run will catch; a careless prompt in a Hamiltonian Monte Carlo or a high-dimensional chapter produces results that look plausible and are wrong.

The second, Collaborating with an LLM on the topic at hand, comes at the end of the chapter: specific prompts, each paired with what to watch for and how to verify. Each prompt is structured as a triple, the prompt itself, the failure modes the model may exhibit, and a verification step the reader runs to catch them. We apply the framework uniformly across the thirteen chapters.

1.4 Reading order

The chapters may be read in order or out of order, subject to the following dependencies.

  • Chapters 1 and 2, the numerical foundations, underpin all the numerical work in chapters 3 through 7.
  • Chapter 3, advanced optimization, feeds chapter 4, the EM algorithm and its extensions, and chapter 9, high-dimensional methods.
  • Chapter 5, Monte Carlo, feeds chapter 6, MCMC, which in turn feeds chapter 7, modern Bayesian computation.
  • Chapters 10 through 13, machine learning, software engineering, reproducible computational environments, and interactive visualization, are largely independent of one another and of the numerical chapters, with two exceptions: chapter 10 uses the optimization tools of chapter 3, and chapter 12 follows naturally from chapter 11.

A reader who follows the dependencies in order treats the book as a course; a reader who picks topics ad hoc treats it as a reference.

1.5 What this book does not cover

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

  • Causal inference computing.
  • Longitudinal data analysis beyond the introductory GLMM material.
  • Missing-data computing in depth.
  • Meta-analysis.

We point to the standard references for each as they arise, and the peer-syllabus survey in docs/syllabi-survey.md documents the rationale.

1.6 Software environment

The book assumes a current R installation, a current Quarto, and the package set used in the introductory volume. New software introduced in this volume is named in the chapter that uses it. The companion Biostatistics Practicum volume documents the workflow, the infrastructure, and the deployment conventions assumed throughout.