Ankenman et al. introduced stochastic kriging as a metamodeling tool for representing stochastic simulation response surfaces, and employed a very simple example to suggest that the use of Common Random Numbers (CRN) degrades the capability of stochastic kriging to predict the true response surface. In this article we undertake an in-depth analysis of the interaction between CRN and stochastic kriging by analyzing a richer collection of models; in particular, we consider stochastic kriging models with a linear trend term. We also perform an empirical study of the effect of CRN on stochastic kriging. We also consider the effect of CRN on metamodel parameter estimation and response-surface gradient estimation, as well as response-surface prediction. In brief, we confirm that CRN is detrimental to prediction, but show that it leads to better estimation of slope parameters and superior gradient estimation compared to independent simulation.
Stochastic kriging is a new metamodeling technique for effectively representing the mean response surface implied by a stochastic simulation; it takes into account both stochastic simulation noise and uncertainty about the underlying response surface of interest. We show theoretically, through some simplified models, that incorporating gradient estimators into stochastic kriging tends to significantly improve surface prediction. To address the issue of which type of gradient estimator to use, when there is a choice, we briefly review stochastic gradient estimation techniques; we then focus on the properties of infinitesimal perturbation analysis and likelihood ratio/score function gradient estimators and make recommendations. To conclude, we use simulation experiments with no simplifying assumptions to demonstrate that the use of stochastic kriging with gradient estimators provides more reliable prediction results than stochastic kriging alone.
One of the most fundamental steps
in risk assessment is to quantify
the exposure–response relationship for the material/chemical
of interest. This work develops a new statistical method, referred
to as SKQ (stochastic kriging with qualitative factors), to synergistically
model exposure–response data, which often arise from multiple
sources (e.g., laboratories, animal providers, and shapes of nanomaterials)
in toxicology studies. Compared to the existing methods, SKQ has several
distinct features. First, SKQ integrates data across multiple sources
and allows for the derivation of more accurate information from limited
data. Second, SKQ is highly flexible and able to model practically
any continuous response surfaces (e.g., dose–time–response
surface). Third, SKQ is able to accommodate variance heterogeneity
across experimental conditions and to provide valid statistical inference
(i.e., quantify uncertainties of the model estimates). Through empirical
studies, we have demonstrated SKQ’s ability to efficiently
model exposure–response surfaces by pooling information across
multiple data sources. SKQ fits into the mosaic of efficient decision-making
methods for assessing the risk of a tremendously large variety of
nanomaterials and helps to alleviate safety concerns regarding the
enormous amount of new nanomaterials.
In this paper, we study the methodological underpinnings of the Morris elementary effects method, a model-free factor-screening technique originally proposed for deterministic simulation experiments, and develop an efficient Morris method–based framework (EMM) for simulation factor screening. Equipped with an efficient cluster-sampling procedure, EMM can simultaneously screen the main and interaction (or nonlinear) effects of all factors and control the overall false discovery rate at a prescribed level. Despite focusing on deterministic simulation experiments, we reveal the connections between EMM (also the Morris method) and other factor-screening methods, such as sequential bifurcation, and examine the resulting implications in the stochastic simulation setting under some commonly stipulated assumptions in design of experiments. Numerical experiments are presented to demonstrate the efficiency and efficacy of EMM.
Stochastic kriging (SK) methodology has been known as an effective metamodeling tool for approximating a mean response surface implied by a stochastic simulation. In this paper we provide some theoretical results on the predictive performance of SK, in light of which novel integrated mean squared error-based sequential design strategies are proposed to apply SK for mean response surface metamodeling with a fixed simulation budget. Through numerical examples of different features, we show that SK with the proposed strategies applied holds great promise for achieving high predictive accuracy by striking a good balance between exploration and exploitation.
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