Abstract
In many cases of statistical interest, observations can be viewed as measurements taken at different times of an underlying unknown function. In health-related fields, such measurements are crucial to the health and well-being of patients. For example, measurements over time of mean arterial blood pressure in pregnant women may help doctors gauge the risks of pre-eclampsia or low birth weight. In this case, the goal is the construction of an individual profile so that any changes in the response can be noted quickly. In a sense, the individual acts as their own referee.
For each individual, the response variable is viewed as a vector of measurements in a fixed time interval. The underlying function is modelled in terms of a set of basis functions, with a sparse latent factor regression model introduced for the coefficients of the basis functions.
Bayesian methods are used to quantify uncertainty in observations, model parameters, and model structure. More precisely, a full Bayesian workflow is implemented that includes inference but also progressive model building, model checking, validation and troubleshooting problems in computation, understanding the model, and model comparison. As Bayesian models are complex in nature, it is imperative their performance can be practically evaluated. Pareto smoothed importance sampling leave-one-out cross-validation is used because it does not require refitting the model multiple times with different subsets of the data. This is applied to the problem of model selection, especially the determination of the number of latent factors in the model.