In defense of theory

This article defends the role of theoretical statistics in modern data science and applied research. It argues that while computational approaches are essential, theory remains crucial for solving non-trivial scientific problems. The author provides two concrete examples from medical research: identifying a flaw in the case-crossover design analysis for air pollution studies and explaining why the bootstrap method fails for certain irregular statistics. The piece emphasizes that theoretical understanding, such as knowing the properties of likelihood scores or the regularity conditions for the bootstrap, is key to reliable data analysis.