It is common for model-based simulations to be reported using prediction interval estimates that characterize the lack of precision associated with the simulated values. When based on Monte-Carlo sampling to approximate the relevant probability density function(s), such estimates can significantly underestimate the width of the prediction intervals, unless the sample size is sufficiently large. Using theoretical arguments supported by numerical experiments, we discuss the nature and severity of this problem, and demonstrate how better estimates of prediction intervals can be achieved by adjusting the interval width to account for the size of the sample used in its construction. Our method is generally applicable regardless of the form of the underlying probability density function, and can be particularly useful when the model is expensive to run and large samples are not available. We illustrate its use via a simple example involving conceptual modeling of the rainfall-runoff response of a catchment.

通常使用预测间隔估计来报告基于模型的模拟，该预测间隔表示表征与模拟值相关联的精度不足的特征。当基于蒙特卡洛采样来近似相关的概率密度函数时，除非样本大小足够大，否则此类估计会大大低估预测间隔的宽度。使用数值实验支持的理论论据，我们讨论了此问题的性质和严重性，并演示了如何通过调整间隔宽度以考虑构造中使用的样本大小来更好地估计预测间隔。我们的方法通常适用，无论潜在的概率密度函数的形式如何，当模型的运行成本很高且无法提供大量样本时，该功能尤其有用。我们通过一个简单的示例来说明其用法，该示例涉及流域降雨-径流响应的概念模型。