Deep Neural Networks (DNNs) have proven excellent performance and are very successful in image classification and object detection. Safety critical industries such as the automotive and aerospace industry aim to develop autonomous vehicles with the help of DNNs. In order to certify the usage of DNNs in safety critical systems, it is essential to prove the correctness of data within the system. In this thesis, the research is focused on investigating the sources of uncertainty, what effects various sources of uncertainty has on NNs, and how it is possible to reduce uncertainty within an NN. Probabilistic methods are used to implement an NN with uncertainty estimation to analyze and evaluate how the integrity of the NN is affected. By analyzing and discussing the effects of uncertainty in an NN it is possible to understand the importance of including a method of estimating uncertainty. Preventing, reducing, or removing the presence of uncertainty in such a network improves the correctness of data within the system. With the implementation of the NN, results show that estimating uncertainty makes it possible to identify and classify the presence of uncertainty in the system and reduce the uncertainty to achieve an increased level of integrity, which improves the correctness of the predictions.