Multiple Hypothesis Testing

Multiple hypothesis testing studies how to make reliable decisions when many claims are tested at once, limiting the chance that apparent discoveries are noise. Common approaches include Benjamini–Hochberg for false discovery rate control, Bonferroni and Holm procedures for family-wise error, and sequential methods based on e-values or martingales. Current work applies these tools to high-dimensional feature selection, structured data, and comparisons of language models, often using sample splitting or selective inference to account for how hypotheses were chosen. A central challenge is preserving power while maintaining valid guarantees under dependence, adaptive selection, and repeated testing.