  New time-domain surveys, such as the Vera C. Rubin Observatory Legacy Survey
of Space and Time (LSST), will observe millions of transient alerts each night,
making standard approaches of visually identifying new and interesting
transients infeasible. We present two novel methods of automatically detecting
anomalous transient light curves in real-time. Both methods are based on the
simple idea that if the light curves from a known population of transients can
be accurately modelled, any deviations from model predictions are likely
anomalies. The first modelling approach is a probabilistic neural network built
using Temporal Convolutional Networks (TCNs) and the second is an interpretable
Bayesian parametric model of a transient. We demonstrate our methods' ability
to provide anomaly scores as a function of time on light curves from the Zwicky
Transient Facility. We show that the flexibility of neural networks, the
attribute that makes them such a powerful tool for many regression tasks, is
what makes them less suitable for anomaly detection when compared with our
parametric model. The parametric model is able to identify anomalies with
respect to common supernova classes with high precision and recall scores,
achieving area under the precision-recall curves (AUCPR) above 0.79 for most
rare classes such as kilonovae, tidal disruption events, intermediate
luminosity transients, and pair-instability supernovae. Our ability to identify
anomalies improves over the lifetime of the light curves. Our framework, used
in conjunction with transient classifiers, will enable fast and prioritised
followup of unusual transients from new large-scale surveys.
