This project aims to quantify estimation uncertainty (a part of epistemic uncertainty that is due to the use of a limited number of ground motion sets). The source codes are programmed in R.

The theoretical background is documented in the paper, C. Wu and H.V.Burton. Effects of probability model misspecification on the number of ground motions required for seismic performance assessment. Earthquake Spectra. DOI: 10.1177/87552930241262044

The functionality of the main script

SE_for_CodeBasedAnalysis.R is to calculate the standard errors of the two parameters in a lognormally distributed probabilistic seismic demand model (PSDM). The parametric PSDM has the functional form: $$P(EDP>edp|IM) = 1- \Phi\left(\frac{\log(edp/m_{EDP|IM})}{\sigma_{\log (EDP)|IM}}\right),$$ where $m_{EDP|IM}$ and $\sigma_{\log(EDP)|IM}$ are the conditional median and dispersion for the EDP of interest. This script is to estimate the standard errors for these two parameters, using either the inverse-Fisher method or the robust method.

SE_for_RiskBasedAnalysis.R is to calculate the standard errors of the mean annual frequency of exceeding a given limit state, $\lambda_{ls}$, calculated through integrating a mean hazard curve and a lognormally distributed fragility function: $$\lambda_{ls} = \int_{im}^{} P(LS >ls|IM=im)|d\lambda(im)| \approx \sum_{i}^{} P(LS>ls|IM=im) |\lambda(im_{i+1}) - \lambda(im_{i})|.$$ This script is to estimate the standard errors for $\lambda_{ls}$, using either the inverse-Fisher method or the robust method.

InformationMatrixTest.R is to perform the Information Matrix test, which was developed by Dhaene and Hoorelbeke (2004) and described in the session 'Information Matrix Test' session in the main text.