## 1 Introduction  
Models play a key role in simulating the behavior of engineering structures, though even very detailed models may fail to represent critical mechanisms. The variety of schemes and uncertainties that are typical of civil structures makes the prediction of the actual mechanical behavior and structural performance a difficult task. All this being said, computer simulations are useful engineering tools to design complex systems and to assess their performance [1; 2; 3]. These simulations aim at reproducing the underlying physical phenomena in question providing a solution for the governing equations. However, accurate modelling of the structural systems requires them to be calibrated and validated with direct observations and measured experimental data [4]. Most calibration methods are essentially regression techniques that estimate the model parameters based on the outputs, and eventually on the input, by means of various optimization algorithms. Some of the classical approaches of parameter estimation include weighted least-squares estimation, best linear unbiased estimation, etc. [4]. Basically, they are optimization problems of minimizing the difference between computed model output and experimental measured data. However, such deterministic approaches bump into some common problems: they are prone to be ill-conditioned, extremely susceptible to errors, and affected by stability issues. As a consequence, a single optimal parameter vector is not sufficient to specify the structural model, but rather a family of all plausible values of the model parameters needs to be identified that are consistent with the observations [5]. Moreover, a common situation in practice is to have limited acquired data and hence sparse datasets. This introduces epistemic uncertainty (lack of knowledge) alongside aleatory uncertainty (natural variability) [6]. All these factors result in uncertainty on model prediction. Therefore, addressing the uncertainty in the model parameters and studying how it influences the uncertainty in the response of the system is crucial and necessary to get accurate predictions with realistic levels of confidence. This evidence naturally leads to the consideration of the problem from a probabilistic perspective. The existing literature on probabilistic calibration is extensive [7; 8; 9] and focuses particularly on Bayesian approaches [10; 11; 12; 13; 14; 15; 16], Bayesian approaches with model class selection [17] and Bayesian filtering methods [18; 19]. A consequence of using imperfect models in the calibration is that the identified parameters may not correspond to their physical namesakes [1]. The resulting posteriors do not necessarily give estimates of the true value of physical parameters, but rather give values which lead the model to best explain the data. In order to estimate the true physical value of parameters, careful thought needs to be taken when considering which parameters to include in the calibration. In addition, the model discrepancy term must be precisely specified to connect model prediction to the observations [6]. In the civil engineering research field, the Bayesian methodology has been used especially for the structural model updating based on experimental dynamic data [5; 20] to update the uncertainty of the mechanical parameters of reinforced concrete (RC) structures [21; 22] and masonry structures [23; 24; 25]. The novelty of this study is the application of this framework on models representing data measured directly on masonry structures during seismic events. The goal is to investigate model-driven seismic structural health monitoring (SHM) procedures by incorporating the posterior uncertainty linked to updated model discrepancy in order to propose its use for the seismic SHM of buildings. This points to the importance of correlating the choice of the discrepancy model function to the degradation amount and to the characteristics of the external seismic input.