Bayesian smooth-and-match inference for ordinary differential equations models linear in the parameters

Saverio Ranciati*, Ernst C. Wit, Cinzia Viroli

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)


Dynamic processes are crucial in many empirical fields, such as in oceanography, climate science, and engineering. Processes that evolve through time are often well described by systems of ordinary differential equations (ODEs). Fitting ODEs to data has long been a bottleneck because the analytical solution of general systems of ODEs is often not explicitly available. We focus on a class of inference techniques that uses smoothing to avoid direct integration. In particular, we develop a Bayesian smooth-and-match strategy that approximates the ODE solution while performing Bayesian inference on the model parameters. We incorporate in the strategy two main sources of uncertainty: the noise level of the measured observations and the model approximation error. We assess the performance of the proposed approach in an extensive simulation study and on a canonical data set of neuronal electrical activity.

Original languageEnglish
Pages (from-to)125-144
Number of pages20
JournalStatistica Neerlandica
Issue number2
Early online date21-Nov-2019
Publication statusPublished - May-2020
Externally publishedYes


  • MCMC
  • penalized splines
  • ridge regression
  • smoothing

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