## 3 Results
### Demonstration on a Case Study  
Having established that the UQ framework can significantly help to gain insight into the uncertainties intrinsic to calibration, thus furnishing a realistic level of confidence on model prediction, this can now be applied to a case study. The aim is to study how the UQ works with an identified hysteretic and degrading model that emulates the experimental response of a real monitored masonry building, the Town Hall of Pizzoli, subjected to its real earthquake recorded data. This is  
Figure 6: Velocity response prediction of the BWBN benchmark model. Figure 7: Posterior samples of the BWBN benchmark model parameters. The vertical lines denote the mean of the distribution (in yellow) and the maximum a posteriori estimate (MAP) (in red). a three-story stone masonry building located northwest of the city of L'Aquila (Abruzzo), which is away from the city. It was built around 1920 and it formerly hosted a school. The structure presents a u-shaped regular plan mainly distributed along one direction, and its elevations are characterized by regular openings distributed along three levels above the ground (the raised ground floor, the first floor and the under-roof floor). The total area is about 770 m\({}^{2}\) while the volume is about 5000 m\({}^{3}\). Figure 8 reports the schematizations of the analyzed building. The Town Hall of Pizzoli belongs to the network of buildings monitored by OSS [26]. The OSS monitors the structure of Pizzoli thanks to a dynamic monitoring system composed of eight accelerometers installed on the building and one placed in the basement. More specifically, a tri-axial accelerometer to record the seismic input in the three space directions is fixed in the basement. On the raised ground floor, no accelerometers are present. On the first floor, three biaxial accelerometers and one monoaxial accelerometer (in X direction) are present to capture the acceleration responses of the first floor in the two horizontal directions. Finally, the same scheme of sensors installed on the first floor is present on the second floor. It is worth noting that the acquisition system and the sensors setup was designed by OSS and represents an input data for our analyses. In this regard, to obtain an optimal positioning of the sensors, a finite element model should be used. In particular, the optimal sensor placement is done recurring to a linear finite element model (using eigen-analysis, singular value decomposition, etc.). The model is often linear to perform this task because for nonlinear analysis the linear elastic component commonly brings the predominant amount of the output variance. The system sampled the signals at 250 Hz, for a total duration of about 50 s for the analyzed earthquake. The acquisition system recorded the sequence that struck central Italy in 2016. For this study, the earthquake acceleration responses of the building recorded on 30 October 2016 were used as reference signals. It is worth noting that accelerometric data are used in this work to define the likelihood function during the calibration. This is true as the use of inter-storey drift in the definition of the likelihood function would require its estimation. This estimate is often complicated because the filtering and integration operation on experimental data usually brings errors during the elaboration, especially with respect to the time alignment of two different recorded signals (quantities that are needed to estimate the inter-storey drift). Since the scope of this study is to show how the discrepancy of models affects the calibration of model parameters value for seismic SHM, only the inter-storey response of the under-roof floor (2 nd DoF) has been considered as reference output quantity. The acceleration of the first floor (1 st DoF) is considered as the input signal of the reference model. The decision to use an inter-storey law is based on the fact that the results of the calibration will be compared with the results of calibration performed with discrepant models.