Automated function prediction (AFP) methods increasingly use knowledge discovery algorithms to map sequence, structure, literature, and/or pathway information about proteins whose functions are unknown into functional ontologies, typically (a portion of) the Gene Ontology (GO). While there are a growing number of methods within this paradigm, the general problem of assessing the accuracy of such prediction algorithms has not been seriously addressed. We present first an application for function prediction from protein sequences using the POSet Ontology Categorizer (POSOC) to produce new annotations by analyzing collections of GO nodes derived from annotations of protein BLAST neighborhoods. We then also present hierarchical precision and hierarchical recall as new evaluation metrics for assessing the accuracy of any predictions in hierarchical ontologies, and discuss results on a test set of protein sequences. We show that our method provides substantially improved hierarchical precision (measure of predictions made that are correct) when applied to the nearest BLAST neighbors of target proteins, as compared with simply imputing that neighborhood's annotations to the target. Moreover, when our method is applied to a broader BLAST neighborhood, hierarchical precision is enhanced even further. In all cases, such increased hierarchical precision performance is purchased at a modest expense of hierarchical recall (measure of all annotations that get predicted at all).