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(Abridged) In tandem with observational datasets, we utilize realistic mockcatalogs, based on a semi-analytic galaxy formation model, constructedspecifically for Pan-STARRS1 Medium Deep Surveys in order to assess theperformance of the Probability Friends-of-Friends (PFOF, Liu et al.) groupfinder, and aim to develop a grouping optimization method applicable to surveyslike Pan-STARRS1. Producing mock PFOF group catalogs under a variety ofphotometric redshift accuracies ({\sigma}{\Delta}z/(1+zs)), we find thatcatalog purities and completenesses from ``good' {\sigma}{\Delta}z/(1+zs)) ~0.01) to ``poor' {\sigma}{\Delta}z/(1+zs)) ~ 0.07) photo-zs gradually degraderespectively from 77% and 70% to 52% and 47%. To avoid model dependency of themock for use on observational data we apply a ``subset optimization' approach,using spectroscopic-redshift group data from the target field to train thegroup finder for application to that field, as an alternative method for thegrouping optimization. We demonstrate this approach using thesespectroscopically identified groups as the training set, i.e. zCOSMOS groupsfor PFOF searches within PS1 Medium Deep Field04 (PS1MD04) and DEEP2 EGS groupsfor searches in PS1MD07. We ultimately apply PFOF to four datasets spanning thephoto-z uncertainty range from 0.01 to 0.06 in order to quantify the dependenceof group recovery performance on photo-z accuracy. We find purities andcompletenesses calculated from observational datasets broadly agree with theirmock analogues. Further tests of the PFOF algorithm are performed via matchesto X-ray clusters identified within the PS1MD04 and COSMOS footprints. Acrossover a decade in group mass, we find PFOF groups match ~85% of X-ray clustersin COSMOS and PS1MD04, but at a lower statistical significance in the latter.

Probability Friends-of-Friends (PFOF) Group Finder: Performance Study and Observational Data Applications on Photometric Surveys