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 VO2, a physiological measure of exercise intensity, using readily available physiological data. Inference was performed using Integrated Nested Laplace Approximation. For practical use by clinicians VO2 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.