  We make use of Kronecker structure for scaling Gaussian Process models to
large-scale, heterogeneous, clinical data sets. Repeated measures, commonly
performed in clinical research, facilitate computational acceleration for
nonlinear Bayesian nonparametric models and enable exact sampling for
non-conjugate inference, when combinations of continuous and discrete endpoints
are observed. Model inference is performed in Stan, and comparisons are made
with brms on simulated data and two real clinical data sets, following a
radiological image quality theme. Scalable Gaussian Process models compare
favourably with parametric models on real data sets with 17,460 observations.
Different GP model specifications are explored, with components analogous to
random effects, and their theoretical properties are described.
