  When mathematical biology models are used to make quantitative predictions
for clinical or industrial use, it is important that these predictions come
with a reliable estimate of their accuracy (uncertainty quantification).
Because models of complex biological systems are always large simplifications,
model discrepancy arises - where a mathematical model fails to recapitulate the
true data generating process. This presents a particular challenge for making
accurate predictions, and especially for making accurate estimates of
uncertainty in these predictions. Experimentalists and modellers must choose
which experimental procedures (protocols) are used to produce data to train
their models. We propose to characterise uncertainty owing to model discrepancy
with an ensemble of parameter sets, each of which results from training to data
from a different protocol. The variability in predictions from this ensemble
provides an empirical estimate of predictive uncertainty owing to model
discrepancy, even for unseen protocols. We use the example of electrophysiology
experiments, which are used to investigate the kinetics of the hERG potassium
ion channel. Here, 'information-rich' protocols allow mathematical models to be
trained using numerous short experiments performed on the same cell. Typically,
assuming independent observational errors and training a model to an individual
experiment results in parameter estimates with very little dependence on
observational noise. Moreover, parameter sets arising from the same model
applied to different experiments often conflict - indicative of model
discrepancy. Our methods will help select more suitable mathematical models of
hERG for future studies, and will be widely applicable to a range of biological
modelling problems.
