Using Discrepancy Theory to Improve the Design of Randomized Controlled Trials - Daniel Spielman

Explore the application of discrepancy theory to enhance randomized controlled trial design in this comprehensive lecture. Delve into the potential outcomes model, experimental design, and average treatment effect. Examine the Thompson estimator, difference of means, and methods for measuring variance. Investigate balanced designs, covariance, and the Gram-Schmidt walk algorithm. Analyze sub-Gaussian tails, algorithm explanations, and projections. Gain insights into variance calculations, ideal cases, and phases of the process. Discover how to achieve better confidence intervals and understand the crucial factors influencing trial outcomes. Learn about orthonormal bases and the potential for improvement in randomized controlled trial methodologies.

Introduction
What are randomized control trials
Potential outcomes model
Experimental design
Average treatment effect
Thompson estimator
Difference of means
Measuring variance
Variance expression
IID case
Balanced design
Covariance
Gramschmidt walk
Variance
Tradeoff parameter
Guarantees
Sub Gaussian tails
Algorithm explanation
Algorithm analysis
Projections
Two crucial factors
Intuition for variance calculation
Ideal case
Phases
Variance bound
Orthonormal basis
Can we improve
The gramschmidt walk
Better confidence intervals