Motivated by the paradigm of event-based monitoring, which can potentially alleviate the inherent bandwidth and energy constraints associated with wireless sensor networks, we consider the problem of joint coding of correlated sources under a cost criterion that is appropriately conditioned on event occurrences. The underlying premise is that individual sensors only have access to partial information and, in general, cannot reliably detect events. Hence, sensors optimally compress and transmit the data to a fusion center, so as to minimize the expected distortion in segments containing events. In this work, we derive and demonstrate the approach in the setting of entropy constrained distributed vector quantizer design, using a modified distortion criterion that appropriately accounts for the joint statistics of the events and the observation data. Simulation results show significant gains over conventional design as well as existing heuristic based methods, and provide experimental ev...