Design-based inference: thoughts, methods, algorithms

In this talk we highlight the coherence between design and analysis of randomized experiments and demonstrate how one drives the other using the Fisherian and Neymanian perspectives. In the first part, we show the connection between design and analysis in the context of the Fisherian randomization test (FRT), simultaneously highlighting some recent interesting findings related to inversion of FRTs, related algorithmic and computational issues and meta-analysis. In the second part, we discuss another connection between the design and analysis from the Neymanian perspective - optimal allocation of units to treatments using randomization-based inference.