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Atrial Fibrillation (AF) is among one of the most common types of heart arrhythmia afflicting more than 3 million people in the U.S. alone. AF is estimated to be the cause of death of 1 in 4 individuals. Recent advancements in Artificial Intelligence (AI) algorithms have led to the capability of reliably detecting AF from ECG signals. While these algorithms can accurately detect AF with high precision, the discrete and deterministic classifications mean that these networks are likely to erroneously classify the given ECG signal. This paper proposes a variational autoencoder classifier network that provides an uncertainty estimation of the network's output in addition to reliable classification accuracy. This framework can increase physicians' trust in using AI-based AF detection algorithms by providing them with a confidence score which reflects how uncertain the algorithm is about a case and recommending them to put more attention to the cases with a lower confidence score. The uncertainty is estimated by conducting multiple passes of the input through the network to build a distribution; the mean of the standard deviations is reported as the network's uncertainty. Our proposed network obtains 97.64% accuracy in addition to reporting the uncertainty.