We present a novel method for the light-curve characterization of Pan-STARRS1 Medium Deep Survey (PS1 MDS) extragalactic sources into stochastic variables (SV) and burst-like (BL) transients, using multi-band image-differencing time-series data. We select detections in difference images associated with galaxy hosts using a star/galaxy catalog extracted from the deep PS1 MDS stacked images, and adopt a maximum a posteriori formulation to model their difference-flux time-series in four Pan-STARRS1 photometric bands g,r,i, and z. We use three deterministic light-curve models to fit burst-like transients and one stochastic light curve model, the Ornstein-Uhlenbeck process, in order to fit variability that is characteristic of active galactic nuclei (AGN). We assess the quality of fit of the models band-wise source-wise, using their estimated leave-out-one cross-validation likelihoods and corrected Akaike information criteria. We then apply a K-means clustering algorithm on these statistics, to determine the source classification in each band. The final source classification is derived as a combination of the individual filter classifications. We use our clustering method to characterize 4361 extragalactic image difference detected sources in the first 2.5 years of the PS1 MDS, into 1529 BL, and 2262 SV, with a purity of 95.00% for AGN, and 90.97% for SN based on our verification sets. We combine our light-curve classifications with their nuclear or off-nuclear host galaxy offsets, to define a robust photometric sample of 1233 active galactic nuclei and 812 supernovae. We use these samples to identify simple photometric priors that would enable their real-time identification in future wide-field synoptic surveys.
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