  Patients who are mechanically ventilated in the intensive care unit (ICU)
participate in exercise as a component of their rehabilitation to ameliorate
the long-term impact of critical illness on their physical function. The
effective implementation of these programmes is hindered, however, by the lack
of a scientific method for quantifying an individual patient's exercise
intensity level in real time, which results in a broad one-size-fits-all
approach to rehabilitation and sub-optimal patient outcomes. In this work we
have developed a Bayesian hierarchical model with temporally correlated latent
Gaussian processes to predict $\dot VO_2$, a physiological measure of exercise
intensity, using readily available physiological data. Inference was performed
using Integrated Nested Laplace Approximation. For practical use by clinicians
$\dot VO_2$ was classified into exercise intensity categories. Internal
validation using leave-one-patient-out cross-validation was conducted based on
these classifications, and the role of probabilistic statements describing the
classification uncertainty was investigated.
