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One of the problems in Bayesian inference is the prior selection. We can categorize different methods for selecting prior into two main groups: informative and non-informative. Here, we have considered an informative method called filters random filed and minimax entropy (FRAME). Despite of its theoretical interest, that method introduces a huge amount of computational burden, which makes it very unsuitable for real-time applications. The main critical point of the method is its parameter estimation part, which plays a major role in its very low speed. In this paper, we have introduced a fast method for parameter estimation to fasten the FRAME approach. Although the kernel of our approach is the Gibbs sampler that intrinsically has very low speed, our proposed method has led to a proper speed.