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Introduction to the Second Half

What the second half is

The first half of this book covers programming, numerical linear algebra, optimization, simulation, the bootstrap, the standard frequentist models, and statistical graphics. It is written for the first quarter of a two-quarter graduate sequence. The second half, which begins here, is written for the second quarter and begins where the first leaves off. In print it is Volume II.

What ‘advanced’ means here

The word ‘advanced’ carries three meanings in the second half, in increasing strength.

The first is a deeper treatment of foundational topics. 16  Numerical Stability and Conditioning and 17  Numerical Linear Algebra in Depth, on numerical stability and numerical linear algebra, revisit material the first half touches but does not treat in depth. Floating-point arithmetic, condition numbers, sparse and iterative solvers, and BLAS-level performance are the fundamentals that everything after them depends on.

The second is topics that exceed introductory scope. 18  Advanced Optimization through 23  Modern Bayesian Computation take up advanced optimization, the EM algorithm and its extensions, Monte Carlo in depth, Bayesian computation, MCMC in depth, and modern Bayesian computation. Each chapter extends the first-half treatment of its topic 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 first half at all. 24  Parallel Computing in R through 33  Advanced Interactive Visualization and Dashboards take up parallel and high-performance computing, high-dimensional methods, machine learning, R package development and testing, software engineering for statisticians, reproducible computational environments, and interactive applications and dashboards. This is ground the first half deliberately sets aside. Each is the kind of topic a practicing biostatistician meets mid-career, and that graduate training ought to prepare them for.

What ‘in the Age of AI’ commits the second half to

The subtitle commits every chapter to two named sections.

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 stakes rise further once the prompt is handed to a coding agent that edits the analysis code and reruns the pipeline unattended, rather than typed into a chat window. In that case nothing forces a human to see the intermediate step where the mistake was made.

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 second half, as in the first.

Reading order

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

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

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.

Software environment

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