The rest of the paper is organized as follows. The second section introduces the proposed method that estimates the Hurst exponent with a Bayesian approach. The third section presents the simulation results and compare the estimation performance of the proposed method to the traditional regression method. The fourth section illustrates an application of the proposed method to a real-life **data** set, a turbulence velocity signal, that is known to possess Hurst exponent H = 1/3. The last section is devoted to the concluding remarks and a future research direction.