# Uncertainty about Uncertainty: Optimal Adaptive Algorithms for Estimating Mixtures of Unknown Coins

19 Apr 2019Jasper C. H. LeePaul Valiant

Given a mixture between two populations of coins, "positive" coins that each have---unknown and potentially different---bias $\geq\frac{1}{2}+\Delta$ and "negative" coins with bias $\leq\frac{1}{2}-\Delta$, we consider the task of estimating the fraction $\rho$ of positive coins to within additive error $\epsilon$. We achieve a tight upper and lower bound of $\Theta(\frac{\rho}{\epsilon^2\Delta^2})$ samples for constant probability of success... (read more)

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