Inverting Random Functions III: Discrete MLE Revisited
  This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2 we investigate a concept of invertibility and the invertibility of the composition of random functions. In Section 3 we resolve some questions concerning the number of samples required to ensure the accuracy of parametric maximum likelihood estimation (MLE). A direct application to phylogeny reconstruction is given. 
Mike A. Steel and Laszlo A. Szekely