Recent years have witnessed quantum computing technologies increasingly move from theoretical proposals to functioning experimental platforms, reaching major milestones such as the demonstration of beyond-classical computational tasks. Despite these exciting advances, current quantum computers experience hardware-level errors which limit their scalability and which must be carefully identified before they can be mitigated. In this talk, I will develop a statistical framework for characterizing errors in quantum devices using an existing experimental platform known as random circuit sampling. Data arising from this experiment can be described through a high-dimensional discrete latent variable model parametrized by the device's error rates. We develop estimators for these error rates which are provably consistent even for large-scale quantum devices. We then apply our methods to benchmark a recent state-of-the-art quantum processor, obtaining a detailed report of error rates which were largely unavailable from past studies. I will close by placing these results in the broader context of my interdisciplinary work in the physical sciences, and by discussing some of my other research interests in nonparametric statistics and statistical optimal transport.