How to Verify Any (Reasonable) Distribution Property: Computationally Sound Argument Systems for Distributions

As statistical analyses become more central to science, industry and society, there is a growing need to ensure correctness of their results. Approximate correctness can be verified by replicating the entire analysis, but can we verify without replication? Building on a recent line of work, we study proof-systems that allow a probabilistic verifier to ascertain that the results of an analysis are approximately correct, while drawing fewer samples and using less computational resources than would be needed to replicate the analysis. We focus on distribution testing problems: verifying that an…