### Table 2: Bayesian Inference when = 0 without Covariate Parameter Point Estimate 95% Credible Set

1996

"... In PAGE 11: ... Tables 4, 6 and 7 include information on generated through simulations as dictated by the data. Table2 presents some Bayesian inference on the coe cients. Table 3 compares classical estimates (mle) for the true contents with their Bayesian counterparts.... ..."

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### Table 3: = 0 without Covariate Parameter Estimated Bayesian Method Classical Inference

1996

"... In PAGE 11: ... Table 2 presents some Bayesian inference on the coe cients. Table3 compares classical estimates (mle) for the true contents with their Bayesian counterparts. The classical estimates in this case are especially undesirable as they do not obey the unit-sum constraint.... ..."

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### Table 3: Parameter Estimates without Bayesian Statistics

### Table 5: = 0 with Covariate Parameter Estimated Classical Inference Bayesian Method 95% Credible Set

1996

"... In PAGE 12: ...quantities when 6 = 0. Table5 examines the log-normal situation with covariate and in this set-up the agreement between the classical and Bayesian estimates for the regression parameters is better. Table 6 concludes the analysis with similar results as above with 6 = 0.... ..."

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### Table 6: Non-zero with Covariate Parameter Estimated Classical Inference Bayesian Method 95% Credible Set

1996

"... In PAGE 12: ... Table 5 examines the log-normal situation with covariate and in this set-up the agreement between the classical and Bayesian estimates for the regression parameters is better. Table6 concludes the analysis with similar results as above with 6 = 0. Classical estimates presented in this Table use ideas to t each ratio to normality as opposed to yielding (joint) g-dimensional multivariate normality.... ..."

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### Table 1: Bayesian inference of singular values, lr, given different rank estimates: Bayesian selection (r = 3), and ARD Property (r = 9). Bayesian selection ARD Property

"... In PAGE 15: ... = 10. True (i.e. the simulated) singular values are given in Table1 together with approximating moments of their posterior distribution (39). Simulated values are clearly within the uncertainty bounds.... In PAGE 15: ... Moments of the transformed distri- butions are displayed in Table 2 and Table 3, together with the projection of the original simulated values in each case. Again, we condition on the two cases of r used in Table1 . Projected true values of Ar and Xr are, in both cases, within the uncertainty bounds of the posteriors (A.... ..."

### Table 14. Intervals for joint pfd: point estimates vs. Bayesian bounds Intervals based on point estimates Intervals based on Bayesian bounds

### Table 2. Point estimates and their variances Method

"... In PAGE 5: ...espectively. The subscript b indicates a Bayesian estimate. It is worth noting that the symmetric form of the non-standard posterior density for the case of a t-Gamma prior density can only be inferred through MCMC simulation. Table2 shows the estimates and their variances for the parameters of the AR(2) model fitted to the Furnas time series. MLE are the maximum likelihood estimates.... In PAGE 6: ...ig. 3. Histograms for the parameters f 1, f 2 and t generated via MCMC simulation using prior density Normal-Gamma. In Table 3, the estimation uncertainty for the estimates in Table2 is easily quantified by the credible intervals. Table 3.... ..."

### Table 3 The proportion of estimated OFV points to the real OFV points after correlation based selection and Bayesian iteration.

"... In PAGE 4: ... In correlation based method OFV N feature points were selected with maximal correlation. Table3 shows the change of this ratio after correlation based selection and Bayesian iteration. Table 2 and 3 clearly shows that after the iterations we can take a useful estimation about the OFV, while other initial statistical values do not concentrate in the OFV.... ..."

### Table 4: Non-zero without Covariate Parameter Estimated Bayesian Method 95% Credible Set

1996

"... In PAGE 12: ...Table4 includes simulation based estimates of all relevant quantities when 6 = 0. Table 5 examines the log-normal situation with covariate and in this set-up the agreement between the classical and Bayesian estimates for the regression parameters is better.... ..."

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