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If we did, we could rewrite log(λ xi j ) so that “random effect” has a zero conditional mean: log(λ xi j ) = β0 + E(log ϑ2i j | G) + β1 log(x) + log(ϑ2i j ) − E(log ϑ2i j | G); in this case β0 and E(log ϑ2i j | G) would be confounded. 4 Data analysis In this section we analyse the Kevlar fibre failure data and compare our results to those obtained previously by Le´on et al. . Model (4) needs to be completed with the specification of G 0 and the prior distribution for β1 . We assume β1 to be normal with mean zero and variance 104 .
More precisely, Z (·) is a zero-mean stationary Gaussian process with constant marginal variance σ 2 and non-negative correlation function between two inputs that depends on their distance and tends towards 1 as the distance moves towards 0. Two different types of Kriging metamodels have been proposed in the literature depending on the functional form of the trend component: • Universal Kriging: the trend depends on x and is modeled in a regressive way: μ(x) = f (x)t β, (1) where f (x) = ( f1 (x), .
Amer. Statist. Assoc. 100, 1278–1291 (2005) 16. : On a class of Bayesian nonparametric estimates I. Density estimates. Ann. Statist. 12, 351–357 (1984) 17. : A sensitivity analysis for Bayesian nonparametric density estimators. Statist. Sinica 19, 685–705 (2009) 18. : Some Developments of the Blackwell-MacQueen Urn Scheme. S. et al. ) Statistics, Probability and Game Theory; Papers in honor of David Blackwell, volume 30 of Lecture Notes-Monograph Series. Institute of Mathematical Statistics, Hayward, California, 245–267 (1996) 19.