Gaussian stochastic process emulation is a powerful tool for approximating computationally intensive computer models. However, estimation of parameters in the GaSP emulator is a challenging task. No closed-form estimator is available, and many numerical problems arise with standard estimates, e.g., the maximum likelihood estimator. In this package, we implement a marginal posterior mode estimator for special priors and parameterizations, an estimation method that meets robust parameter estimation criteria; mathematical reasons are provided therein to explain why robust parameter estimation can greatly improve predictive performance of the emulator. In addition, inert inputs (inputs that almost have no effect on the variability of a function) can be identified from the marginal posterior mode estimation, at no extra computational cost. The package also implements the parallel partial Gaussian stochastic process (PP GaSP) emulator for scenarios where computer models have multiple outputs on e.g., spatio-temporal coordinates. The package can be operated in a default mode, but also allows numerous user specifications, such as the capability of specifying trend functions and noise terms. Examples are studied herein to highlight the performance of the package in terms of out-of-sample prediction.

翻译：高斯随机过程仿真是一种近似计算密集型计算机模型的有力工具。然而，GaSP仿真器中参数的估计是一个具有挑战性的任务。由于不存在封闭形式的估计量，且标准估计方法（如最大似然估计）会引发众多数值问题。在本软件包中，我们针对特定先验和参数化方法实现了边际后验众数估计，这是一种满足稳健参数估计准则的估计方法；我们提供了数学解释，阐明为何稳健参数估计能显著提升仿真器的预测性能。此外，边际后验众数估计能够以零额外计算成本识别惰性输入（即对函数变异性几乎无影响的输入）。该软件包还实现了并行偏高斯随机过程（PP GaSP）仿真器，适用于计算机模型在时空坐标等场景下具有多输出的情形。该软件包既可默认运行，也允许用户进行大量自定义设置，例如指定趋势函数和噪声项的能力。本文通过示例研究了该软件包在样本外预测方面的性能表现。