  Bayesian modelling of dynamic systems must achieve a compromise between
providing a complete mechanistic specification of the process while retaining
the flexibility to handle those situations in which data is sparse relative to
model complexity, or a full specification is hard to motivate. Latent force
models achieve this dual aim by specifying a parsimonious linear evolution
equation which an additive latent Gaussian process (GP) forcing term. In this
work we extend the latent force framework to allow for multiplicative
interactions between the GP and the latent states leading to more control over
the geometry of the trajectories. Unfortunately inference is no longer
straightforward and so we introduce an approximation based on the method of
successive approximations and examine its performance using a simulation study.
