There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources of predictive uncertainty, namely aleatoric uncertainty (inherent data variability) and epistemic uncertainty (model-related uncertainty). Together with Bayesian methods, applied as an approximation, we build a framework that allows one to generate different predictive uncertainty measures. We validate our method on image datasets by evaluating its performance in detecting out-of-distribution and misclassified instances using the AUROC metric. The experimental results confirm that the measures derived from our framework are useful for the considered downstream tasks.