Fast Bayesian Functional Data Analysis: Application to basal body temperature data.

In many clinical settings, it is of interest to monitor a bio-marker over time for a patient in order to estimate that patient's trajectory and to identify or predict clinically important features. For example, these features may correspond to a low or high point in the trajectory or to a sudden change. There is a need for fast algorithms for estimating functional trajectories while borrowing information from other patients about the shape and location of features in the function. Borrowing of information is crucial when observations are sparse and the interest is in prediction. In this paper, we presents an application of a fast approximate Bayes functional data analysis relying on spareness-favoring hierarchical priors for P-spline basis coefficients. The proposed method is used to rapidly estimate individual-specific functions. We present an application to basal body temperature (bbt) data.