Abstract:
ABSTRACT
This thesis considered a flexible two-stage statistical approach to multi-task
modeling of multivariate physiological vital signs using GP regression, in which
the joint use of nonparametric and Bayesian GP regression methods are ex-
plored. In the first stage, nonparametric schemes based on expected value con-
tribution statistics for fusing multiple physiological vital signs observed over
common time-stamps into a composite vital sign are developed. In the second
stage, an appropriate Bayesian Gaussian process regression model is developed
for the fused vital sign trajectory in relation to the common observation time-
stamps. The relationship existing among the multiple vital signs and available
non-time-dependent covariates is modeled with the aid of OGK statistics via
the covariance function of the assumed GP. Both Variational Bayes and MCMC
methods are developed for parameter inference. The coupling of density-based
data fusing methods and GP modeling allowed automated extreme value control
within both the response and predictor spaces; response dimension reduction;
data reduction in the response space and principled modeling of smoothness of
the physiological trend. Using both simulation and real data application, the
utility of the proposals is illustrated. In terms of fusing of multivariate vital
signs, results show that the probability distribution-based features provide a rich
source of appealing functional features with the natural ability to ensure that ex-
treme observations are utilized with their effects controlled automatically. For
the GP modeling of fused vital signs, the results show that both VB and MCMC
algorithms exhibit better fitting performance in terms of MSFE, MAFE, and
SMAFE. Thus, the double-stage modeling approach exhibits a great potential
for handling multi-task GP regression within the single-task GP framework.
