Title: Effective Uncertainty Estimation with Evidential Models for Open-World Recognition. Abstract: Reliable uncertainty estimation is crucial when deploying a classifier in the wild. In this paper, we tackle the challenge of jointly quantifying in-distribution and out-of-distribution (OOD) uncertainties. To this end, we leverage the second-order uncertainty representation provided by evidential models and we introduce KLoS, a Kullback–Leibler divergence criterion defined on the class-probability simplex. By keeping the full distributional information, KLoS captures class confusion and lack of evidence in a single score. A crucial property of KLoS is to be a class-wise divergence measure built from in-distribution samples and to not require OOD training data, in contrast to current second-order uncertainty measures. We further design an auxiliary neural network, KLoSNet, to learn a refined criterion directly aligned with the evidential training objective. In the realistic context where no OOD data is available during training, our experiments show that KLoSNet outperforms first-order and second-order uncertainty measures to simultaneously detect misclassifications and OOD samples. When training with OOD samples, we also observe that existing measures are brittle to the choice of the OOD dataset, whereas KLoS remains more robust.