As Bayesian deep learning (BDL) combines the complementary advantages of the Bayesian method and deep learning (DL), it becomes a powerful tool for uncertainty modeling and inference of complex problems. In this study, a BDL framework based on t distribution and the cyclic stochastic gradient Hamiltonian Monte Carlo sampling algorithm is constructed, and a measure of uncertainty is given in view of data uncertainty and model uncertainty. To verify the validity and applicability of the framework, this study constructs corresponding BDL models based on the artificial neural network (ANN), convolutional neural network (CNN), and recurrent neural network (RNN) separately and applies these models to the prediction of 15 global stock indices. The empirical results reveal that 1) the framework is applicable under ANN, CNN, and RNN, and the prediction effect of all indices is excellent; 2) in terms of prediction accuracy and applicability, the BDL models based on t distribution have significant advantages over those based on normal distribution; 3) the MAE under a given uncertainty threshold is better than the original MAE, which indicates that the measure of uncertainty defined in this study is effective and is of great significance to uncertainty modeling. In view of the advantages of the BDL framework in forecasting accuracy, easy to expand and providing measurement of forecasting uncertainty, it has a broad application prospect in finance and other fields with complex data characteristics.