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Table 2

Summaries of the Bayesian estimation.

copula prior mean s-m sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
Frank NI 23.936 0.062 2.185 −28.396 −25.384 −23.854 −22.440 −19.903 1255 1.006
Frank I 24.108 0.061 2.139 −28.376 −25.593 −24.057 −22.614 −20.035 1216 1.001
Gaussian NI 0.953 0.000 0.007 −0.965 −0.957 −0.953 −0.948 −0.937 1458 1.000
Gaussian I 0.953 0.000 0.007 −0.965 −0.958 −0.954 −0.949 −0.937 1210 1.002

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 letter the Bayesian estimates of θ for Frank and ρ for Gaussian copula, by quadratic loss function on left, by multi linear loss function on right. Non-Informative (NI) prior on top and Informative (I) prior on bottom.