Efficient Bayesian inference for ordinary differential equation models from experimental data with uncertain measurement times

Abstract

Time-resolved measurements are central to calibrating mechanistic dynamical models, but current inference frameworks typically assume that reported measurement times are exact. In practice, actual sampling times may deviate from reported times because of sample-handling delays, imper-fect synchronization, or reporting errors. Here, we present a Bayesian framework for parameter inference in ordinary differential equation models that explicitly accounts for uncertainty in measurement times. We formulate latent measurement times as random variables and derive a joint and marginalized posterior. To compute the marginal likelihood efficiently, we augment the original dynamical system with additional state variables that evaluate the required integrals during numerical simulation. This reduces the dimensionality of the estimation problems and allows for efficient and reliable Markov chain Monte Carlo sampling. Across synthetic examples and a published model of carotenoid cleavage in Arabidopsis thaliana, neglecting time uncertainty led to biased estimates and overconfident uncertainty quantification, whereas the proposed marginalized formulation recovered reliable parameter estimates while substantially improving sampling efficiency and scalability. These results identify measurement time uncertainty as an important source of variability in dynamic modeling and establish posterior marginalization as a practical strategy for robust mechanistic inference.