Deep Probabilistic Models (DPM) based on arithmetic circuits representation, such as Sum-Product Networks (SPN) and Probabilistic Sentential Decision Diagrams (PSDD), have shown competitive performance in several machine learning tasks with interesting properties (Poon and Domingos 2011; Kisa et al. 2014). Due to the high number of parameters and scarce data, DPMs can produce unreliable and overconfident inference. This research aims at increasing the robustness of predictive inference with DPMs by obtaining new estimators of the predictive uncertainty. This problem is not new and the literature on deep models contains many solutions. However the probabilistic nature of DPMs offer new possibilities to achieve accurate estimates at low computational costs, but also new challenges, as the range of different types of predictions is much larger than with traditional deep models. To cope with such issues, we plan on investigating two different approaches. The first approach is to perform a global sensitivity analysis on the parameters, measuring the variability of the output to perturbations of the model weights. The second approach is to capture the variability of the prediction with respect to changes in the model architecture. Our approaches shall be evaluated on challenging tasks such as image completion, multilabel classification.