Data availability—including the type, quantity, and quality of data—both determines and often limits the use of mathematical models. Therefore, careful planning of data collection in advance is essential to maximize the utility of mathematical models in addressing specific research questions. In this talk, I will present some of my work on designing data collection strategies and experiments to infer characteristics of interest in biomedical applications. First, I will introduce a Bayesian information-theoretic framework to determine effective scanning protocols for cancer patients. This work is motivated by the limited temporal resolution of clinical data: the amount of data that can be practically collected during therapy is severely constrained by financial costs and patient burden. To address this challenge, we propose a modified mutual information function with a temporal penalty term that accounts for the loss of temporal data. The effectiveness of this framework is demonstrated in optimizing scanning schedules for radiotherapy and androgen suppression therapy patients. Second, I will present inference methods for characterizing interactions within heterogeneous populations. Our approach can separately estimate intra- and inter-species interactions in a birth–death process by quantifying higher statistical moments of the trajectories—information that cannot be extracted from the mean trajectory alone.