Optimal experimental design for parameter estimation in the presence of observation noise

Mathematical models play an increasingly important role in interpreting experiments, particularly in biology and ecology. Accurate parameter estimation is vital for quantifying observed behaviours, inferring unmeasurable ones, and making predictions. However, the reliability of parameter estimates depends on the quality, quantity, and timing of collected data-a concept known as parameter identifiability. For many dynamical models, parameter uncertainty can shift dramatically as observation times vary. In this study, we explore local sensitivity measures from the Fisher information matrix and global measures from Sobol' indices to examine how parameter uncertainty varies as a result of changes in the number and timing of observations. We then embed these measures within an optimisation algorithm to identify observation schedules that minimise uncertainty. Applying this framework to models with both correlated and uncorrelated observation noise reveals that noise correlations can substantially affect optimal observation times. This underscores the importance of correctly accounting for the observation noise structure when designing experiments.