GNGTS 2013 - Atti del 32° Convegno Nazionale

parameter g (peak ground acceleration, response spectrum ordinate, macroseismic intensity, etc.) deduced by applying the i-th procedure can be considered as a conditional probability in the form P(g|H i ) . This conditional probability parameterizes aleatory uncertainty managed by the i-th procedure. In this context, the unconditional hazard estimate P(g) can be given in the form (1) with the condition where the probability P(H i ) is the degree of belief associated to the procedure H i . This last condition implies that at least one PSHA procedure exists among the M considered, that can be considered a reliable one. It is worth to note that the distribution P(g) preserves its meaning of a probability distribution (over the proper domain of g values) and also accounts for epistemic uncertainty associated to the presence of a multiplicity of PSHA procedures: it represents a “comprehensive” hazard curve. This curve is not affected by uncertainty: it represents overall uncertainty about future seismic occurrences. By considering the definition of unconditional PSHA estimate in Eq. (1) and being each term P(g|H i ) entirely defined in the frame of the i-th computational scheme H i , the development comprehensive PSHA outcome P(g) relies on the definition of the values to be attributed to P(H i ) . Assessment of these values can be addressed as the “Scoring” PSHA procedures. This can be achieved basically in two ways. The first one is “ex-ante”, that is by considering inherent properties of the PSHA procedure, their internal robustness of their coherency with current knowledge about underlying physical process evaluated by panels of scientists. The second procedure is “ex-post” and consider a comparison of PSHA models outcomes (“forecasts”) with observations: being incorrect to use the term “validation” for this kind of meta-analysis (Oreskes et al. , 1994), the term “Testing” should be preferred for this kind of procedure. The problem of judging heuristic value of competing models (being probabilistic or not) is quite general and has been also addressed by Lipton (2005). A major conclusion is that, despite of the fact that ex-post tests based on the comparisons of “forecasts” and observations cannot be judged as inherently better, these can be considered as more “robust” against “fudging”. The typical example of ex-ante scoring is the so-called “logic-tree” approach based on the combination of expert judgments about single elements of the considered PSHA procedure (e.g., SSHAC, 1997). An example of “ex-post” approach are empirical testing procedures (e.g., Beauval, 2011). Despite of their strong differences and backgrounds, “ex-ante” and “ex-post” approaches can be seen as complementary in the frame of a Bayesian view. In the case that a testing set of S occurrences e S is known (the “evidence” E ), the “ex-post” degree of belief in the i-th procedure can be expressed in terms of the conditional probability P ( H i | E ) given by (2) where P* ( H i ) is the prior degree of belief associated to H i and corresponds to the ex-ante evaluation. The term P ( E | H i ) represents the likelihood of the evidence E in the case that the H i model holds. This term actually represents the probability that the model H i associates to the evidence E : in other terms it represents the “forecast” of the model about that specific scenario. The term 1/ P ( E ) is a simple normalization factor. In the case that M mutually exclusive competing PSHA models exist and that this set is complete, one has (3) 10 GNGTS 2013 S essione 2.1