Stat 9917

Topics in Selective Inference and Predictive Inference

Description

This PhD course covers topics in selective inference and distribution-free predictive inference. The first half focuses on selective inference, introducing problems and tools in multiple testing, post-selection inference, and adaptive/sequential inference. The second half centers on distribution-free predictive inference, with an emphasis on conformal inference. Throughout, we highlight recent advances, practical considerations, and open problems in both areas.

Syllabus

• Multiple testing: global null, FWER, FDR, local FDR
• Post-selection inference, sequential testing
• Testing with e-values
• Empirical Bayes, compound decision-making
• Permutation test, conformal inference
• Distribution-free predictive inference

Grading

Grade will be based on a course project. Each student is expected to complete a research project that is related in some way to the themes and topics of the course. Projects may be theoretical or empirical (ideally a mix of both), and students are encouraged to build on or connect to their thesis research. The instructor will meet with students individually to discuss project ideas and provide feedback on progress throughout the semester. The grading components are:

• 10% - Proposal (due Feb 16, 2026): Submit a short report (no more than 1 page) stating the research problems that you plan to work on. Describe why they are important or interesting and provide some appropriate references.
• 10% - Progress report (due Mar 23, 2026): Submit a progress report (no more than 3 pages) summarizing what you have completed so far, any preliminary results, and your updated plan for the remainder of the project.
• 40% - Final presentation (in class): Give an in-class presentation on your project, outlining the problem, approach, main findings, and takeaways. Final timing may be adjusted depending on enrollment.
• 40% - Final report (due May 4, 2026): Submit a final project report summarizing your goals, methodology, main results, and conclusions. Discuss limitations and possible next steps. Include complete references and, when relevant, provide a link to reproducible code and data

We use canvas for submission.

Reading

The following references are related to the topics covered in the class.

• Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. B. Efron, IMS Monographs.
• Hypothesis Testing with E-values. A. Ramdas and R. Wang, Foundations and Trends in Statistics.
• Theoretical foundations of conformal prediction. Anastasios N. Angelopoulos, Rina Foygel Barber, and Stephen Bates.

Resources

The international seminar on selective inference (ISSI) is a weekly online seminar on selective inference and related topics. Every week, an invited speaker will give a 45-min talk, followed by a 15-min discussion.

Schedule