<p>Bayesian deep learning (BDL) has become a potent technique for quantifying uncertainty in classification tasks, outperforming the traditional deep learning (DL) networks in terms of providing reliable results. Approximate Bayesian inference techniques have proven useful in making uncertainty estimation in the results of DL networks not intractable. This BDL gives more confidence in the results of DL networks and in adopting them in real-world applications, thus making informed decisions. Application of BDL based on appropriate Bayesian inference technique in important areas such as agriculture, especially regarding plant diseases, is essential to ensure responsible decisions. This paper presents a reliable approach to further improve the quantification of uncertainty in wheat disease detection called explainable Bayesian convolutional neural network (EBCNN). This approach relies on one of the DL networks, which is the convolutional neural network (CNN), and to make it able to detect the level of confidence in its results, a Bayesian inference technique was used. The Bayesian inference technique used is based on the Gaussian noise (GN) method, which is a method commonly used to prevent overfitting of DL networks. The proposed EBCNN can classify wheat diseases with high efficiency and accuracy of 93.44%. The proposed EBCNN can demonstrate both trust in its correct predictions and lack of confidence in its incorrect predictions. The proposed EBCNN can also provide an explanation for its results by revealing the characteristics that were relied upon in diagnosing wheat diseases.</p>