Conformal Statistical Inference: From Theory to Practice

Conformal inference (also known as conformal prediction) is a flexible and distribution-free framework for constructing prediction sets with finite-sample coverage guarantees. This tutorial provides a comprehensive introduction that bridges theory and practice.

What’s Covered

• Foundations of Conformal Inference — exchangeability, nonconformity scores, and coverage guarantees
• Split Conformal Prediction (SCP) — the computationally efficient workhorse method
• Conformal Quantile Regression (CQR) — adaptive prediction intervals handling heteroscedasticity
• Full Conformal Prediction — using all data for calibration (computationally intensive but theoretically optimal)
• Jackknife+ — leave-one-out conformal with improved coverage properties

Resources

• 📘 Comprehensive Guide (English): Interactive HTML notebook
• 🎓 Tutorial Slides (Spanish): Quarto RevealJS presentation
• 💻 Source Code: Available in the tutorial repository

Implementation

All methods are implemented with reproducible code in R and Python, with detailed explanations of each algorithm step. The tutorial slides in Spanish are designed for a biostatistics master’s level audience at the University of Granada.

Keywords: Conformal inference, conformal prediction, prediction intervals, uncertainty quantification, distribution-free inference, machine learning, statistical learning theory.