Title: Fast methods for identifying high dimensional systems using
observations

Advisors: Roshan Joseph Vengazhiyil and Jianjun Shi

Committee members: Dr. Jianjun Shi, Dr. Roshan Vengazhiyil, Dr. C.-F.
Jeff Wu, Dr. Kamran Paynabar and Dr. Richard K. Archibald (Oak Ridge
National Labs).

Date, time, and venue: Wednesday, February 25, 2015, 11:00AM, GC 304

Thesis summary:
Computational modeling is a popular tool to understand a diverse set of
complex systems. The output from a computational model depends on a set
of parameters which are unknown to the designer, but a modeler can
estimate them by collecting physical data. In the second chapter of this
thesis, we study the action potential of ventricular myocytes and our
parameter of interest is a function as opposed to a scalar or a set of
scalars. We develop a new modeling strategy to nonparametrically study
the functional parameter using Bayesian inference with Gaussian process
priors. We also devise a new Markov chain Monte Carlo sampling scheme to
address this unique problem.

In the more general case, computational simulation is expensive.
Emulators avoid the repeated use of a stochastic simulation by
performing a designed experiment on the computer simulation and
developing a predictive distribution.  Random field models are
considered the standard in analysis of computer experiments, but the
current framework fails in high dimensional scenarios because of the
cost of inference. The third chapter of this thesis shows by using a
class of experimental designs, the computational cost of inference from
random fields scales significantly better in high dimensions. Exact
prediction and likelihood evaluation with close to half a million design
points is possible in seconds using only a laptop computer. Compared to
the more common space-filling designs, the proposed designs are shown to
be competitive in terms of prediction accuracy through simulation and
analytic results.

The fourth chapter of this thesis proposes a method to construct an
emulator for a stochastic simulation. Existing emulators have focused on
estimation of the mean of the simulation output, but this work presents
an emulator for the distribution of the output in a nonparametric
setting. This construction provides both an explicit distribution and a
fast sampling scheme. Beyond describing the emulator, this work
demonstrates that the emulator's convergence rate is asymptotically rate
optimal among all possible emulators using the same sample size.  
Lastly, the fifth chapter of this work investigates the use of a
modified version of the above method to study patterns of defects on
products. We achieve efficient inference on the defect patterns by
developing a novel estimate of an inhomogeneous point process that is
both computationally tractable and asymptotically appealing.