We present a Bayesian framework to learn prior and posterior distributions for latent variable models. Our goal is to deal with model regularization and achieve desirable prediction using heterogeneous speech data. A variational Bayesian expectation-maximization algorithm is developed to establish a latent variable model based on the exponential family distributions. This algorithm does not only estimate model parameters but also their hyperparameters which reflect the model uncertainties. The uncertainty is compensated to construct a variety of regularized models. We realize this full Bayesian framework for uncertainty decoding of speech signals. Compared to maximum likelihood method and Bayesian approach with heuristically-selected hyperparameters, the proposed method achieves higher speech recognition accuracy especially in case of sparse and noisy training data.