Hausdorff Distance evaluation of orthodontic accessories' streaking artifacts in 3D model superimposition

The aim of this study was to determine whether image artifacts caused by orthodontic metal accessories interfere with the accuracy of 3D CBCT model superimposition. A human dry skull was subjected three times to a CBCT scan: at first without orthodontic brackets (T1), then with stainless steel brackets bonded without (T2) and with orthodontic arch wires (T3) inserted into the brackets' slots. The registration of image surfaces and the superimposition of 3D models were performed. Within-subject surface distances between T1-T2, T1-T3 and T2-T3 were computed and calculated for comparison among the three data sets. The minimum and maximum Hausdorff Distance units (HDu) computed between the corresponding data points of the T1 and T2 CBCT 3D surface images were 0.000000 and 0.049280 HDu, respectively, and the mean distance was 0.002497 HDu. The minimum and maximum Hausdorff Distances between T1 and T3 were 0.000000 and 0.047440 HDu, respectively, with a mean distance of 0.002585 HDu. In the comparison between T2 and T3, the minimum, maximum and mean Hausdorff Distances were 0.000000, 0.025616 and 0.000347 HDu, respectively. In the current study, the image artifacts caused by metal orthodontic accessories did not compromise the accuracy of the 3D model superimposition. Color-coded maps of overlaid structures complemented the computed Hausdorff Distances and demonstrated a precise fusion between the data sets.

Comparison between the complete Bayesian method and empirical Bayesian method for ARCH models using Brazilian financial time series

In this work we compared the estimates of the parameters of ARCH models using a complete Bayesian method and an empirical Bayesian method in which we adopted a non-informative prior distribution and informative prior distribution, respectively. We also considered a reparameterization of those models in order to map the space of the parameters into real space. This procedure permits choosing prior normal distributions for the transformed parameters. The posterior summaries were obtained using Monte Carlo Markov chain methods (MCMC). The methodology was evaluated by considering the Telebras series from the Brazilian financial market. The results show that the two methods are able to adjust ARCH models with different numbers of parameters. The empirical Bayesian method provided a more parsimonious model to the data and better adjustment than the complete Bayesian method.