Premium
Bayesian smooth‐and‐match inference for ordinary differential equations models linear in the parameters
Author(s) -
Ranciati Saverio,
Wit Ernst C.,
Viroli Cinzia
Publication year - 2020
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12192
Subject(s) - ode , ordinary differential equation , bayesian inference , smoothing , inference , mathematics , computer science , bottleneck , bayesian probability , mathematical optimization , algorithm , differential equation , artificial intelligence , statistics , mathematical analysis , embedded system
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.