We develop a theory of estimation when in addition to a sample of $n$ observed outcomes the underlying probabilities of the observed outcomes are known, as is typically the case in the context of numerical simulation modeling, e.g. in epidemiology. For this enriched information framework, we design unbiased and consistent ``probability-based'' estimators whose variance vanish exponentially fast as $n\to\infty$, as compared to the power-law decline of classical estimators' variance.

翻译：我们提出一种估计理论，该理论适用于除了$n$个观测结果样本外，还已知观测结果的基础概率的情况——这在数值模拟建模（例如流行病学）中较为常见。针对这种信息增强框架，我们设计了无偏且一致的“基于概率”的估计量，其方差随$n\to\infty$呈指数级衰减，而经典估计量的方差则呈幂律下降。