Oscillation detection with period uncertainty and a limited sampling budget

Most rhythm detection experiments involve measurements collected at regular time-intervals. These equispaced designs will fail to detect oscillations at particular acrophases and frequencies even when oscillation amplitude is large. The spurious false negatives pose a challenge for studies aiming to determine the presence or absence of oscillations across a range of parameters. Here, we present a method to construct sampling schemes that are robust to parameter uncertainty, and demonstrate their improvements relative to equispaced designs. We prove that maximizing the worst-case statistical power is equivalent to a mixed-integer quadratically-constrained programming problem with convex relaxation. Using this equivalence, we construct optimal and near-optimal designs for a range of experimental conditions. Our method also allows us to include regularization and sampling constraints, ensuring that improving statistical power via measurement scheduling does not introduce unnecessary complexity in the design.