  Inference for mechanistic models is challenging because of nonlinear
interactions between model parameters and a lack of identifiability. Here we
focus on a specific class of mechanistic models, which we term stable
differential equations. The dynamics in these models are approximately linear
around a stable fixed point of the system. We exploit this property to develop
fast approximate methods for posterior inference. We illustrate our approach
using simulated data on a mechanistic neuroscience model with EEG data. More
generally, stable differential equation models and the corresponding inference
methods are useful for analysis of stationary time-series data. Compared to the
existing state-of-the art, our methods are several orders of magnitude faster,
and are particularly suited to analysis of long time-series (>10,000
time-points) and models of moderate dimension (10-50 state variables and 10-50
parameters.)
