In this paper, we propose an autoregressive stochastic generative model for images. This modelshould be one of the most basic models for the new type of lossless image compression which explicitly assume the stochastic generative model. We can easily expand it and theoretically interpret theimplicitly assumed stochastic generative models in the various previous predictive coding methods as the expanded versions of our model. Moreover, we can utilize the achievements in the related fields where the linear regression analysis and its expansion are studied to construct the Bayes codes for these generative models. As an example, we expand our generative model from the one with normalnoise to the one with the t-distributed noise. Then, we construct the sub-optimal Bayes codes for this generative model by utilizing the variational Bayesian method.