Deep Bayesian neural network has aroused a great attention in recent years since it combines the benefits of deep neural network and probability theory. Because of this, the network can make predictions and quantify the uncertainty of the predictions at the same time, which is important in many life-threatening areas. However, most of the recent researches are mainly focusing on making the Bayesian neural network easier to train, and proposing methods to estimate the uncertainty. I notice there are very few works that properly discuss the ways to measure the performance of the Bayesian neural network. Although accuracy and average uncertainty are commonly used for now, they are too general to provide any insight information about the model. In this paper, we would like to introduce more specific criteria and propose several metrics to measure the model performance from different perspectives, which include model calibration measurement, data rejection ability and uncertainty divergence for samples from the same and different distributions.
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