This dissertation presents novel methodologies in the field of stochastic computer model calibration and uncertainty quantification. Simulation models are widely used in studying physical systems, which are often represented by a set of mathematical equations. Inference on true physical system (unobserved or partially observed) is drawn based on the observations from corresponding computer simulation model. These computer models are calibrated based on limited ground truth observations in order produce realistic predictions and associated uncertainties. Stochastic computer model differs from traditional computer model in the sense that repeated execution results in different outcomes from a stochastic simulation. This additional uncertainty in the simulation model requires to be handled accordingly in any calibration set up.

Gaussian process (GP) emulator replaces the actual computer simulation when it is expensive to run and the budget is limited. However, traditional GP interpolator models the mean and/or variance of the simulation output as function of input. For a simulation where marginal gaussianity assumption is not appropriate, it does not suffice to emulate only the mean and/or variance. We present two different approaches addressing the non-gaussianity behavior of an emulator, by (1) incorporating quantile regression in GP for multivariate output, (2) approximating using finite mixture of gaussians. These emulators are also used to calibrate and make forward predictions in the context of an Agent Based disease model which models the Ebola epidemic outbreak in 2014 in West Africa.

The third approach employs a sequential scheme which periodically updates the uncertainty inn the computer model input as data becomes available in an online fashion. Unlike other two methods which use an emulator in place of the actual simulation, the sequential approach relies on repeated run of the actual, potentially expensive simulation.