Uncertainties in ground motion prediction in probabilistic seismic hazard analysis (PSHA) of civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 47

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Linear AY92 Linear R97 Quadratic AY92 Quadratic R97

2.5 Infl uence of accounting for magnitude uncertainty during the
derivation of a prediction equation for Arias intensity. Here the
reduction is expressed by way of comparing the computed inter-event
standard deviations using different methods. AY92 stands for
Abrahamson & Youngs (1992), R97 stands for Rhoades (1997). The
boxplots are generated for inter-event residuals for both linear and
quadratic models. The quadratic model residuals correspond to an
extension of the method of Rhoades (1997) developed by Stafford
(2006).

by Stafford (2006) that either include linear or quadratic magnitude scaling.
In the case of the quadratic model while the fi gure attributes this to Rhoades
(1997), the regression method implemented was an extension for quadratic
magnitude scaling proposed by Stafford (2006). It is clear that when mag-
nitude uncertainty is accounted for and the quadratic functional form is
implemented a signifi cant reduction in the computed inter-event standard
deviation can be obtained.

2.4.3 Prediction intervals and parameter uncertainty

Once the regression approach has been selected and the dataset chosen one
is able to conduct the regression analysis in order to obtain estimates of the
model coeffi cients. While there are a number of algorithms available for
this purpose, all decent algorithms will enable the analyst to simultaneously
compute a covariance matrix associated with the estimated model coeffi -
cients. The trace of this matrix is generally used to compute the standard
errors, and p -values of the coeffi cients in order to test for their statistical
signifi cance. The off-diagonal terms of the matrix are also inspected to