Consistency and Uniform Bounds for Heteroscedastic Simulation Metamodeling and Their Applications

Heteroscedastic metamodeling has gained popularity as an effective tool for analyzing and optimizing complex stochastic systems. A heteroscedastic metamodel provides an accurate approximation of the input-output relationship implied by a stochastic simulation experiment whose output is subject to input-dependent noise variance. Several challenges remain unsolved in this field. First, in-depth investigations into the consistency of heteroscedastic metamodeling techniques, particularly from the sequential prediction perspective, are lacking. Second, sequential heteroscedastic metamodel-based level-set estimation (LSE) methods are scarce. Third, the increasingly high computational cost required by heteroscedastic Gaussian process-based LSE methods in the sequential sampling setting is a concern. Additionally, when constructing a valid uniform bound for a heteroscedastic metamodel, the impact of noise variance estimation is not adequately addressed. This dissertation aims to tackle these challenges and provide promising solutions. First, we investigate the information consistency of a widely used heteroscedastic metamodeling technique, stochastic kriging (SK). Second, we propose SK-based LSE methods leveraging novel uniform bounds for input-point classification. Moreover, we incorporate the Nystrom approximation and a principled budget allocation scheme to improve the computational efficiency of SK-based LSE methods. Lastly, we investigate empirical uniform bounds that take into account the impact of noise variance estimation, ensuring an adequate coverage capability.