Maximum entropy method helps study multifractal processes

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Abstract

Many natural phenomena exhibit scaling behavior, in which parts of the system resemble the whole. Topography is one example—in some landscapes, shapes seen on a small scale look similar to shapes seen at larger scales. Some processes with scaling behavior are multifractal processes, in which the scaling parameters are described by probability distributions. Nieves et al. show that a method known as the maximum entropy method, which has been applied in information theory and statistical mechanics, can be applied generally to study the statistics of multifractal processes. The authors note that the method, which could be applied to a wide variety of geophysical systems, makes it possible to infer information on multifractal processes even beyond scales where observations are available. (Geophysical Research Letters, doi:10.1029/2011GL048716, 2011)

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