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In many fields of application, dynamic processes that evolve through time arewell described by systems of ordinary differential equations (ODEs). Theanalytical solution of the ODEs is often not available and different methodshave been proposed to infer these quantities: from numerical optimization toregularized (penalized) models, these procedures aim to estimate indirectly theparameters without solving the system. We focus on the class of techniques thatuse smoothing to avoid direct integration and, in particular, on a BayesianSmooth-and-Match strategy that allows to obtain the ODEs' solution whileperforming inference on models that are linear in the parameters. Weincorporate in the strategy two main sources of uncertainty: the noise level inthe measurements and the model error. We assess the performance of the proposedapproach in three different simulation studies and we compare the results on adataset on neuron electrical activity.

Bayesian Smooth-and-Match strategy for ordinary differential equations models that are linear in the parameters