GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 2.2 431 In order to assess the reliability of the proposed procedures, an investigation of the confidence intervals of the observed damage and of individual regression coefficients is carried out. Regression lines of the observed damage for two of the twenty-one considered mechanisms are shown in Fig. 2 together with confidence intervals and, for comparison reasons, prediction bounds. Fig. 2 - Regression lines of the observed damage with scatter plot of the data with confidence (in red) and prediction (in dashed blue) intervals for: a) mechanism no. 1 (overturning of the façade); b) mechanism no. 6 (shear in longitudinal walls). a) b) The prediction bounds provide information on individual predictions of the accounted dependent variable, giving a range of values where an additional observation of the variable can be expected to be located. In fact, prediction intervals provide a range of values where we can expect future observations to fall and are useful when the aim is using the model to predict individual values of the response. As shown in Fig. 2, the confidence interval is associated to a smaller range of values, because it is an interval estimate for an average value rather than an interval estimate for a single observation, as provided by the prediction intervals. This result confirms the recommendation of using territorial scale analyses only for average estimation rather than individual forecasts. The confidence intervals of each regression coefficient have been computed, in addition to the mean estimate, to investigate the expected range of dependent variables value. In Fig. 3, the confidence limits of the two vulnerability modifiers, poor masonry quality and connections, found to be crucial for most mechanisms, are presented, showing acceptable limit intervals, with few mechanisms presenting large intervals due to specific conditions of the sample size. Fig. 3 - Boxplot of confidence intervals of specific vulnerability modifiers for each considered mechanism: a) poor masonry quality; b) connections. a) b) Acknowledgements. This work has been partially carried out under the program “Dipartimento di Protezione Civile – Consorzio RELUIS”. The opinions expressed in this publication are those of the authors and are not necessarily endorsed by the Dipartimento di Protezione Civile.