Fast methods for identifying high dimensional systems using observations

Abstract

This thesis proposes new analysis tools for simulation models in the presence of data. To achieve a representation close to reality, simulation models are typically endowed with a set of inputs, termed parameters, that represent several controllable, stochastic or unknown components of the system. Because these models often utilize computationally expensive procedures, even modern supercomputers require a nontrivial amount of time, money, and energy to run for complex systems. Existing statistical frameworks avoid repeated evaluations of deterministic models through an emulator, constructed by conducting an experiment on the code. In high dimensional scenarios, the traditional framework for emulator-based analysis can fail due to the computational burden of inference. This thesis proposes a new class of experiments where inference from half a million observations is possible in seconds versus the days required for the traditional technique. In a case study presented in this thesis, the parameter of interest is a function as opposed to a scalar or a set of scalars, meaning the problem exists in the high dimensional regime. This work develops a new modeling strategy to nonparametrically study the functional parameter using Bayesian inference.

Stochastic simulations are also investigated in the thesis. I describe the development of emulators through a framework termed quantile kriging, which allows for non-parametric representations of the stochastic behavior of the output whereas previous work has focused on normally distributed outputs. Furthermore, this work studied asymptotic properties of this methodology that yielded practical insights. Under certain regulatory conditions, there is the following result: By using an experiment that has the appropriate ratio of replications to sets of different inputs, we can achieve an optimal rate of convergence. Additionally, this method provided the basic tool for the study of defect patterns and a case study is explored.