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Seismic exposure of buildings presents difficult engineering challenges. The principles of seismic design involve structures that sustain damage and still protect inhabitants. Precise and accurate knowledge of the residual capacity of damaged structures is essential for informed decision-making regarding clearance for occupancy after major seismicevents. Unless structures are permanently monitored, modal properties derived from ambient vibrations are most likely the only source of measurement data that are available. However, such measurement data are linearly elastic and limited to a low number of vibration modes. Structural identification using hysteretic behavior models that exclusively relies on linear measurement data is a complex inverse engineering task that is further complicated by modeling uncertainty. Three structural identification methodologies that involve probabilistic approaches to data interpretation are compared: error-domain model falsification, Bayesian model updating with traditional assumptions as well as modified Bayesian model updating. While noting the assumptions regarding uncertainty definitions,athe accuracy and robustness of identification and subsequent predictions are compared. A case study demonstrates limits on non-linear parameter identification performance and identification of potentially wrong prediction ranges for inappropriate model uncertainty distributions.