Statistical approaches. One of the most common statistical procedures adopted to estimate Mmax in low-seismicity areas, like SCRs, is the so-called EPRI approach (Xxxxxxxx et al., 1994). It has been applied in several PSH studies worldwide and, in Europe, in the framework of the PEGASOS project for Switzerland (Xxxxxxxx and Xxxxxxxx, 2009; Xxxxxx and Xxxxxx, 2009; Xxxxxx et al., 2009). This approach provides a probability distribution of Mmax taking into account the large relevant uncertainty. It is based on information coming from the analysis of a global data set of seismicity in SCRs (Xxxxxxxx et al., 1994), updated with local data available for the seismic source of interest (i.e. magnitude values of the earthquakes occurred inside the source zone) in the frame of Bayesian statistics. The basic concept is to compensate the small seismicity sample of the study area by considering observations from tectonically analogous regions worldwide. In particular, the procedure requires defining a “prior” probability distribution for Mmax, which is derived from the statistical analysis of the global data set, and then combining the prior distribution with a source zone specific likelihood function to obtain a posterior distribution for Mmax to be used in PSHA. Two prior worldwide normal distributions were derived by Xxxxxxxx et al. (1994): one for extended and another for non-extended continental crust, which are characterized by different mean and standard error values (i.e. mean Mmax=6.4 vs 6.3, standard deviation=0.84 vs 0.5, respectively). The likelihood function for the study area is computed from the reported magnitudes for earthquakes occurred inside the zone, assuming an exponential frequency-magnitude distribution. This function, describing the relative likelihood of different values of Mmax given the local seismicity sample, is zero for magnitudes lower than the largest observed magnitude in the area, is peaked about the latter, and then decays with a shape depending on the number of data available for the zone and the b-value of the frequency-magnitude distribution. The posterior Mmax probability distribution is then derived by multiplying the prior distribution by the source-specific likelihood function. In case of very small seismicity samples, the shape of the posterior distribution is largely controlled by the selected prior one, except for truncation below the largest observed magnitude inside the zone. The obtained probability distribution is finally discretized at suita...
Statistical approaches. All statistical analyses for this study were performed using the statistical package STATA 10.0 (STATA, 2007). The two overarching statistical approaches applied to all three empirical studies are detailed below. Firstly, statistical analyses using data collected from the E-Risk cohort was complicated because participants were twin pairs growing up in the same family. To control for these non-independent observations, analyses were adjusted with tests based on the sandwich or Xxxxx/White variance estimator (Xxxxxxxx, 2000), a method that is available in the statistical package STATA
