  We derive a statistical model for estimation of a dendrogram from single
linkage hierarchical clustering (SLHC) that takes account of uncertainty
through noise or corruption in the measurements of separation of data. Our
focus is on just the estimation of the hierarchy of partitions afforded by the
dendrogram, rather than the heights in the latter. The concept of estimating
this "dendrogram structure'' is introduced, and an approximate maximum
likelihood estimator (MLE) for the dendrogram structure is described. These
ideas are illustrated by a simple Monte Carlo simulation that, at least for
small data sets, suggests the method outperforms SLHC in the presence of noise.
