  Ordinary differential equation models are used to describe dynamic processes
across biology. To perform likelihood-based parameter inference on these
models, it is necessary to specify a statistical process representing the
contribution of factors not explicitly included in the mathematical model. For
this, independent Gaussian noise is commonly chosen, with its use so widespread
that researchers typically provide no explicit justification for this choice.
This noise model assumes `random' latent factors affect the system in ephemeral
fashion resulting in unsystematic deviation of observables from their modelled
counterparts. However, like the deterministically modelled parts of a system,
these latent factors can have persistent effects on observables. Here, we use
experimental data from dynamical systems drawn from cardiac physiology and
electrochemistry to demonstrate that highly persistent differences between
observations and modelled quantities can occur. Considering the case when
persistent noise arises due only to measurement imperfections, we use the
Fisher information matrix to quantify how uncertainty in parameter estimates is
artificially reduced when erroneously assuming independent noise. We present a
workflow to diagnose persistent noise from model fits and describe how to
remodel accounting for correlated errors.
