Optimal Experimental Design for Big Data: Applications in Brain Imaging

Replicability, the ability to replicate scientific findings, is a prerequisite for scientific discovery and clinical utility. Troublingly, we are in the midst of a replicability crisis. A key to replicability is that multiple measurements of the same item (e.g., experimental sample or clinical participant) under fixed experimental constraints are relatively similar to one another. Thus, statistics that quantify the relative contributions of accidental deviations--such as measurement error--as compared to systematic deviations--such as individual differences--are critical. We demonstrate that existing replicability statistics, such as intra-class correlation coefficient and fingerprinting, fail to adequately differentiate between accidental and systematic deviations in very simple settings. We therefore propose a novel statistic, discriminability, which quantifies the degree to which an individuals samples are relatively similar to one another, without restricting the data to be univariate, Gaussian, or even Euclidean. Using this statistic, we introduce the possibility of optimizing experimental design via increasing discriminability and prove that optimizing discriminability improves performance bounds in subsequent inference tasks. In extensive simulated and real datasets (focusing on brain imaging and demonstrating on genomics), only optimizing data discriminability improves performance on all subsequent inference tasks for each dataset. We therefore suggest that designing experiments and analyses to optimize discriminability may be a crucial step in solving the replicability crisis, and more generally, mitigating accidental measurement error. Author SummaryIn recent decades, the size and complexity of data has grown exponentially. Unfortunately, the increased scale of modern datasets brings many new challenges. At present, we are in the midst of a replicability crisis, in which scientific discoveries fail to replicate to new datasets. Difficulties in the measurement procedure and measurement processing pipelines coupled with the influx of complex high-resolution measurements, we believe, are at the core of the replicability crisis. If measurements themselves are not replicable, what hope can we have that we will be able to use the measurements for replicable scientific findings? We introduce the "discriminability" statistic, which quantifies how discriminable measurements are from one another, without limitations on the structure of the underlying measurements. We prove that discriminable strategies tend to be strategies which provide better accuracy on downstream scientific questions. We demonstrate the utility of discriminability over competing approaches in this context on two disparate datasets from both neuroimaging and genomics. Together, we believe these results suggest the value of designing experimental protocols and analysis procedures which optimize the discriminability.