How do we expose the underlying dynamics of the human body when direct measurement is difficult? From the fragile lungs of extremely preterm infants to the complex processes of the human brain, clinical data is often noisy, indirect, and difficult to interpret. This talk explores how integrating mechanistic mathematical modeling with data-driven statistical inference can bridge the gap between raw biological signals and patient-specific clinical decision making. Specifically, this talk will briefly explore mechanistic and data-driven approaches to two case studies: i) the suppressed respiratory system of the preterm infant and ii) Parkinsonian spiking dynamics in macaque basal ganglia. Computational approaches such as these are increasingly implemented to understand human pathophysiology, but corresponding models depend on reliable estimation of model parameters from available data, which raises two challenges in model identification: parameter identifiability and parameter sensitivity, both of which determine whether parameter estimation is even feasible in a given model. By tackling these challenges with robust mathematical frameworks for model analysis, we can explore resulting models for behavioral interactions between model components, which would otherwise be impossible in a physical setting. This talk will briefly explore distinct approaches to estimating patient- specific parameter values while addressing these challenges in both mathematical (respiratory study) and statistical (Parkinsonian study) modeling frameworks.