A Bayesian analysis of scale - invariant processes Report

We have demonstrated that the Maximum Entropy (ME) principle in the context of Bayesian probability theory can be used to derive the probability distributions of those processes characterized by its scaling properties including multiscaling moments and geometric mean. We started from a proof-of-concept case of a power-law probability distribution, followed by the general case of multifractality aided by the wavelet representation of the cascade model. The ME formalism leads to the probability distribution of the multiscaling parameter and those of incremental multifractal processes at different scales. Compared to other methods, the ME method significantly reduces computational cost by leaving out unimportant details. The ME distributions have been evaluated against the empirical histograms derived from the drainage area of river network, soil moisture and topography. This analysis supports the assertion that the ME principle is a universal and unified framework for modeling processes governed by scale-invariant laws. The ME theory opens new possibilities of extracting information of multifractal processes beyond the scales of observation. Conference Name: BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 31 Conference Date: July 09, 2011 A Bayesian analysis of scale-invariant processes Veronica Nieves, Jingfeng Wang, and Rafael L. Bras Citation: AIP Conf. Proc. 1443, 56 (2012); doi: 10.1063/1.3703620 View online: http://dx.doi.org/10.1063/1.3703620 View Table of