Inverting Random Functions II: Explicit Bounds for Discrete Maximum Likelihood Estimation, with Applications

In this paper we study inverting random functions under the maximum likelihood estimation (MLE) criterion in the discrete setting. In particular, we consider how many independent evaluations of the random function at a particular element of the domain are needed for reliable reconstruction of that element. We provide explicit upper and lower bounds for MLE, both in the nonparametric and parametric setting, and give applications to coin-tossing and phylogenetic tree reconstruction.