Random geometric mean model

If one assumes a random distribution of components, the film permeability can be estimated using the weighted geometric mean of the polymer permeabilities via a model known as the Geometric Mean Model ... 

Figure 7.16 Histogram of posterior predictive check based on the observed data in Table 7.4. Concentration data were simulated for 26 subjects under the original experimental design and sampling times at each dose using population values and variance components randomly drawn from the bootstrap distribution of the final model parameter estimates (FOCE-I Table 7.5). The geometric mean concentration at 6-h postdose (top) and AUC to 12-h postdose (bottom) was calculated. This process was repeated 250 times.

A common means to perform such mapping is to use an approximate method like the Nataf s model (Liu and Der Kiureghian 1986). Once the random variables involved in Equation 1 have been expressed into the standard normal space, it is possible to define the design point (x ) using a geometrical or probabilistic interpretation (see, e.g. (Freudenthal 1956)). In the geometrical interpretation, the design point is defined as the realization in the standard normal space which lies on the limit state function... 

Probabilistic response analysis consists of computing the probabilistic characterization of the response of a specific structure, given as input the probabilistic characterization of material, geometric and loading parameters. An approximate method of probabilistic response analysis is the mean-centred First-Order Second-Moment (FOSM) method, in which mean values (first-order statistical moments), variances and covariances (second-order statistical moments) of the response quantities of interest are estimated by using a mean-centred, first-order Taylor series expansion of the response quantities in terms of the random/uncertain model parameters. Thus, this method requires only the knowledge of the first- and second-order statistical moments of the random parameters. It is noteworthy that often statistical information about the random parameters is limited to first and second moments and therefore probabilistic response analysis methods more advanced than FOSM analysis cannot be fully exploited. 

Evolutionary frequency response function Evolutionary power spectral density function Gaussian zero-mean random models of seismic accelerations Non-geometric spectral moments Stochastic analysis... 

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