  Historically, light curve studies of supernovae (SNe) and other transient
classes have focused on individual objects with copious and high
signal-to-noise observations. In the nascent era of wide field transient
searches, objects with detailed observations are decreasing as a fraction of
the overall known SN population, and this strategy sacrifices the majority of
the information contained in the data about the underlying population of
transients. A population level modeling approach, simultaneously fitting all
available observations of objects in a transient sub-class of interest, fully
mines the data to infer the properties of the population and avoids certain
systematic biases. We present a novel hierarchical Bayesian statistical model
for population level modeling of transient light curves, and discuss its
implementation using an efficient Hamiltonian Monte Carlo technique. As a test
case, we apply this model to the Type IIP SN sample from the Pan-STARRS1 Medium
Deep Survey, consisting of 18,837 photometric observations of 76 SNe,
corresponding to a joint posterior distribution with 9,176 parameters under our
model. Our hierarchical model fits provide improved constraints on light curve
parameters relevant to the physical properties of their progenitor stars
relative to modeling individual light curves alone. Moreover, we directly
evaluate the probability for occurrence rates of unseen light curve
characteristics from the model hyperparameters, addressing observational biases
in survey methodology. We view this modeling framework as an unsupervised
machine learning technique with the ability to maximize scientific returns from
data to be collected by future wide field transient searches like LSST.
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