Thus, we develop a Bayesian scaling estimation method with non-decimated wavelet transform (NDWT) motivated by real-life signals that are known to possess a certain theoretical degree of self-similarity. Bayesian approaches have been previously employed in this context. The Hurst exponent for Gaussian **data** was estimated with a Bayesian model in [11,2,4]. Holan et al. [7] developed a hierarchical Bayesian model to estimate the parameter of stationary long-memory processes. A Baysian model for the parameter estimation of auto-regressive fractionally integrated moving average (ARFIMA) processes [9] are discussed in [6,19,16]. These models are based on time domain data. However, the de-correlation property of wavelet transforms facilitates a simplified model construction, and multiple wavelet-based Bayesian techniques has been developed. Based on a Bayesian approach, Vannucci and Corradi [23] estimated parameters for long memory process with a recursive algorithm and Markov chain Monte Carlo (MCMC) sampling. A Baysian wavelet model for ARFIMA processes is illustrated in [10].