Draft, May 2026

Multiplicity, Selection, and Modern Statistical Inference

An in-progress draft. Topics include multiple testing, false discovery rates, e-values, knockoffs, conformal prediction, debiased inference, and selective inference.

Download draft (PDF)

Current draft contents (subject to change)

• Preface
• Notation
• Introduction
• Global testing
• Simes and higher criticism
• FWER, closure methods, and graphical procedures
• FDR and the Benjamini-Hochberg procedure
• FDR under dependence and empirical Bayes
• Structured and hierarchical FDR
• E-values and safe testing
• Conditional randomization tests and knockoffs
• Conformal prediction
• Debiased Lasso
• Selective inference
• Applications: genomics and large language models

This is an early draft and likely contains errors, gaps, and rough sections. Comments, corrections, and suggestions are very welcome — please email zhangxiany@stat.tamu.edu.

Not a final edition or publisher-ready manuscript. Bibliography and citation metadata may still need work.

The draft grew out of notes for STAT 689 and will be used for the course next semester.

Suggested citation: Zhang, X. (2026). Multiplicity, Selection, and Modern Statistical Inference. Draft version, May 2026.