  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.
