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Accession Number ADA586988
Title Bayesian Analysis of Scale-Invariant Processes.
Publication Date 2012
Media Count 10p
Personal Author J. Wang R. L. Bras V. Nieves
Abstract 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.
Keywords Bayes theorem
Bayesian statistics
Environmental sciences
Maximum entropy
Multifractality
Probability
Probability distribution functions
Scale invariant laws
Statistics

 
Source Agency Non Paid ADAS
NTIS Subject Category 72F - Statistical Analysis
Corporate Author Georgia Tech Research Corp., Atlanta.
Document Type Technical report
Title Note Conference paper.
NTIS Issue Number 1405
Contract Number W911NF-12-1-0095 W911NF-07-1-0126

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