Recent research development has demonstrated the advantages of deep learning models in prediction tasks on electronic health records (EHR) in the medical domain. However, the prediction results tend to be difficult to explain due to the complex neuron structures. Without explainability and transparency, deep learning models are not trustworthy or reliable for making real-world decisions, especially the high-stakes ones in the healthcare domain. To improve the trustworthiness of the deep learning model, quantifying the uncertainty is crucial.In this dissertation work, we proposed several Bayesian Neural Network (BNN) structures to estimate the data uncertainty and model uncertainty associated with the EHR data and deep learning models, respectively. We also proposed Variational Neural Network (VNN) algorithms to estimate the uncertainty of the variables to investigate the medical and temporal features that contribute the most to the patient-level uncertainty. In order to verify the validity of the uncertainty estimations, we designed a series of experiments to examine the computational results against widely accepted facts about uncertainty. We also conducted post-hoc analysis to evaluate whether the proposed models tend to specialize in one or more patient subgroups, at the cost of model performance on others, as well as whether the treatment (improving uncertainty in one subgroup) will mitigate such performance cost. The experiment results have confirmed the validity of our computational approaches. Finally, we conducted a user study to understand the clinicians' perception of the proposed uncertainty models.