Knowledge of forces, exerted on the brain tissue during the performance of neurosurgical tasks, is critical for quality assurance, case rehearsal, and training purposes. Quantifying the interaction forces has been made possible by developing SmartForceps, a bipolar forceps retrofitted by a set of strain gauges. The forces are estimated using voltages read from strain gauges. We therefore need to quantify the force-voltage relationship to estimate the interaction forces during microsurgery. This problem has been addressed in the literature by following the physical and deterministic properties of the force-sensing strain gauges without obtaining the precision associated with each estimate. In this paper, we employ a probabilistic methodology by using a nonparametric Bootstrap approach to obtain both point and interval estimates of the applied forces at the tool tips, while the precision associated with each estimate is provided. To show proof-of-concept, the Bootstrap technique is employed to estimate unknown forces, and construct necessary confidence intervals using observed voltages in data sets that are measured from the performance of surgical tasks on a cadaveric brain. Results indicate that the Bootstrap technique is capable of estimating tool-tissue interaction forces with acceptable level of accuracy compared to the linear regression technique under the normality assumption.

Quantifying the tool–tissue interaction forces in surgery can be used in the training process of novice surgeons to help them better handle surgical tools and avoid exerting excessive forces. A significant challenge concerns the development of proper statistical learning techniques to model the relationship between the true force exerted on the tissue and several outputs read from sensors mounted on the surgical tools. We propose a nonparametric bootstrap technique and a Bayesian multilevel modeling methodology to estimate the true forces. We use the linear exponential loss function to asymmetrically penalize the over and underestimation of the applied forces to the tissue. We incorporate the direction of the force as a group factor in our analysis. A weighted approach is used to account for the nonhomogeneity of read voltages from the surgical tool. Our proposed Bayesian multilevel models provide estimates that are more accurate than those under the maximum likelihood and restricted maximum likelihood approaches. Moreover, confidence bounds are much narrower and the biases and root mean squared errors are significantly smaller in our multilevel models with the linear exponential loss function.

Copulas are powerful explanatory tools for studying dependence patterns in multivariate data. While the primary use of copula models is in multivariate dependence modelling, they also offer predictive value for regression analysis. This article investigates the utility of copula models for model‐based predictions from two angles. We assess whether, where, and by how much various copula models differ in their predictions of a conditional mean and conditional quantiles. From a model selection perspective, we then evaluate the predictive discrepancy between copula models using in‐sample and out‐of‐sample predictions both in bivariate and higher‐dimensional settings. Our findings suggest that some copula models are more difficult to distinguish in terms of their overall predictive power than others, and depending on the quantity of interest, the differences in predictions can be detected only in some targeted regions. The situations where copula‐based regression approaches would be advantageous over traditional ones are discussed using simulated and real data. The Canadian Journal of Statistics 47: 8–26; 2019 © 2018 Statistical Society of Canada