Bayesian Approach to Hurst Exponent Estimation

Fractal investigation of a signal often involves estimating its fractal dimension or Hurst exponent H when considered as a sample of a fractional process. Fractional Gaussian noise (fGn) belongs to the family of self-similar fractional processes and it is dependent on parameter H. There are variety of traditional methods for Hurst exponent estimation. Our novel approach is based on zero-crossing principle and signal segmentation. Thanks to the Bayesian analysis, we present a new axiomatically based procedure of determining the expected value of Hurst exponent together with its standard deviation and credible intervals. The statistical characteristics are calculated at the interval level at first and then they are used for the deduction of the aggregate estimate. The methodology is subsequently used for the EEG signal analysis of patients suffering from Alzheimer disease.