Deep learning (DL), which involves powerful black box predictors, has achieved a remarkable performance in medical image analysis, such as segmentation and classification for diagnosis. However, in spite of these successes, these methods focus exclusively on improving the accuracy of point predictions without assessing the quality of their outputs. Knowing how much confidence there is in a prediction is essential for gaining clinicians' trust in the technology. In this article, we propose an uncertainty estimation framework, called MC-DropWeights, to approximate Bayesian inference in DL by imposing a Bernoulli distribution on the incoming or outgoing weights of the model, including neurones. We demonstrate that by decomposing predictive probabilities into two main types of uncertainty, aleatoric and epistemic, using the Bayesian Residual U-Net (BRUNet) in image segmentation. Approximation methods in Bayesian DL suffer from the "mode collapse" phenomenon in variational inference. To address this problem, we propose a model which Ensembles of Monte-Carlo DropWeights by varying the DropWeights rate. In segmentation, we introduce a predictive uncertainty estimator, which takes the mean of the standard deviations of the class probabilities associated with everyThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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