Table 3
Summaries of the Bayesian estimation.
prior | mean | s–m | sd | 2.5% | 25% | 50% | 75% | 97.5% | n_eff | Rhat | |
---|---|---|---|---|---|---|---|---|---|---|---|
Case VT vs. VF – see Table 1 | |||||||||||
Gaussian | NI | 0.856 | 0.001 | 0.043 | 0.752 | 0.834 | 0.863 | 0.886 | 0.916 | 1161 | 1.000 |
Gaussian | I | 0.859 | 0.001 | 0.040 | 0.765 | 0.838 | 0.865 | 0.887 | 0.918 | 1198 | 1.003 |
Gumbel H | NI | 3.023 | 0.012 | 0.445 | 2.243 | 2.707 | 3.001 | 3.325 | 3.938 | 1315 | 1.003 |
Gumbel H | I | 3.021 | 0.012 | 0.444 | 2.222 | 2.712 | 3.005 | 3.298 | 3.931 | 1320 | 1.001 |
H × VF vs. Dmax – see Table 2 (left) | |||||||||||
Gaussian | NI | 0.696 | 0.003 | 0.088 | 0.490 | 0.648 | 0.712 | 0.760 | 0.822 | 1167 | 1.002 |
Gaussian | I | 0.707 | 0.002 | 0.082 | 0.506 | 0.663 | 0.722 | 0.765 | 0.824 | 1305 | 1.000 |
Gumbel H | NI | 2.100 | 0.009 | 0.317 | 1.512 | 1.881 | 2.089 | 2.302 | 2.743 | 1158 | 1.003 |
Gumbel H | I | 2.111 | 0.009 | 0.319 | 1.540 | 1.883 | 2.089 | 2.317 | 2.805 | 1222 | 1.001 |
Hf vs. Dmax – see Table 2 (right) | |||||||||||
Gaussian | NI | 0.768 | 0.002 | 0.067 | 0.612 | 0.732 | 0.779 | 0.817 | 0.864 | 1286 | 1.002 |
Gaussian | I | 0.771 | 0.002 | 0.065 | 0.618 | 0.736 | 0.782 | 0.819 | 0.864 | 1192 | 1.003 |
Gumbel H | NI | 2.392 | 0.010 | 0.358 | 1.746 | 2.135 | 2.385 | 2.629 | 3.120 | 1273 | 1.001 |
Gumbel H | I | 2.399 | 0.012 | 0.362 | 1.742 | 2.144 | 2.372 | 2.642 | 3.135 | 959 | 1.001 |
n_eff: final number of simulations used for the estimation; sd: standard deviation; s–m = sd/n_eff1/2; Rhat: potential scale reduction factor on split chains (at convergence, Rhat = 1). In bold, the Bayesian estimates of ρ for Gaussian copula and θ for Gumbel–Hougaard copula, by quadratic loss function on left, by multilinear loss function on right. On the top, Non-Informative (NI) prior; on the bottom, Informative (I).
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