There are two major types of uncertainty one can model.

Credal predictors are models that are aware of epistemic uncertainty and produce a convex set of probabilistic predictions. They offer a principled way to quantify predictive epistemic uncertainty (EU) and have been shown to improve model robustness in various settings. However, most state-of-the-art methods mainly define EU as disagreement caused by random training initializations, which mostly reflects sensitivity to optimization randomness rather than uncertainty from deeper sources. To address this, we define EU as disagreement among models trained with varying relaxations of the i.i.d. assumption between training and test data. Based on this idea, we propose CreDRO, which learns an ensemble of plausible models through distributionally robust optimization. As a result, CreDRO captures EU not only from training randomness but also from meaningful disagreement due to potential distribution shifts between training and test data. Empirical results show that CreDRO consistently outperforms existing credal methods on tasks such as out-of-distribution detection across multiple benchmarks and selective classification in medical applications.

We study post-calibration uncertainty for trained ensembles of classifiers. Specifically, we consider both aleatoric (label noise) and epistemic (model) uncertainty. Among the most popular and widely used calibration methods in classification are temperature scaling (i.e., pool-then-calibrate) and conformal methods. However, the main shortcoming of these calibration methods is that they do not balance the proportion of aleatoric and epistemic uncertainty. Not balancing these uncertainties can severely misrepresent predictive uncertainty, leading to overconfident predictions in some input regions while being underconfident in others. To address this shortcoming, we present a simple but powerful calibration algorithm Joint Uncertainty Calibration (JUCAL) that jointly calibrates aleatoric and epistemic uncertainty. JUCAL jointly calibrates two constants to weight and scale epistemic and aleatoric uncertainties by optimizing the negative log-likelihood (NLL) on the validation/calibration dataset. JUCAL can be applied to any trained ensemble of classifiers (e.g., transformers, CNNs, or tree-based methods), with minimal computational overhead, without requiring access to the models' internal parameters. We experimentally evaluate JUCAL on various text classification tasks, for ensembles of varying sizes and with different ensembling strategies. Our experiments show that JUCAL significantly outperforms SOTA calibration methods across all considered classification tasks, reducing NLL and predictive set size by up to 15% and 20%, respectively. Interestingly, even applying JUCAL to an ensemble of size 5 can outperform temperature-scaled ensembles of size up to 50 in terms of NLL and predictive set size, resulting in up to 10 times smaller inference costs. Thus, we propose JUCAL as a new go-to method for calibrating ensembles in classification.

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these subprocesses may be inherently unknown or too computationally intensive to directly embed in the simulation model. Replacing these elements with estimated or learned approximations introduces a form of epistemic uncertainty that we refer to as submodel uncertainty. This paper investigates how submodel uncertainty affects the estimation of system performance metrics. We develop a framework for quantifying submodel uncertainty in stochastic simulation models and extend the framework to digital-twin settings, where simulation experiments are repeatedly conducted with the model initialized from observed system states. Building on approaches from input uncertainty analysis, we leverage bootstrapping and Bayesian model averaging to construct quantile-based confidence or credible intervals for key performance indicators. We propose a tree-based method that decomposes total output variability and attributes uncertainty to individual submodels in the form of importance scores. The proposed framework is model-agnostic and accommodates both parametric and nonparametric submodels under frequentist and Bayesian modeling paradigms. A synthetic numerical experiment and a more realistic digital-twin simulation of a contact center illustrate the importance of understanding how and how much individual submodels contribute to overall uncertainty.

However, the design of methods for learning credal set predictors remains a challenging problem. In this paper, we make use of conformal prediction for this purpose.