(eng): The problem of estimating parameters of an auto-regression model in a Bayesian paradigm has been solved before, when the model has innovations coming from exponential family. The main reason for choosing exponential family was the simplicity of computation and the fact that Gaussian distribution, often found in nature due to existence of limit theorems, is also a member of this family. Applications of modeling to data, where the distribution of innovations is known to be heavy-tailed calls for a method, more robust with respect to possible outliers. We choose the 1-D innovations of the model to be Laplace distributed, choose a Bayesian conjugate prior to such a model distribution and try to compute the resulting filtration, when new data of a realization of an adjacent random process arrive. The computation of the resultant posterior distribution of the parameters of the model is still computationally tractable as will be shown.