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Distances in Probability Space and the Statistical Complexity Setup

AuthorsKowalski, Andres M.; Martin, Maria T.; Plastino, A.; Rosso, Osvaldo A.; Casas, Montserrat
KeywordsGeneralized statistical complexity
Information theory
Selection of the probability distribution
Issue Date3-Jun-2011
PublisherMultidisciplinary Digital Publishing Institute
CitationEntropy 13(6), 1055-1075 (2011)
AbstractStatistical complexity measures (SCM) are the composition of two ingredients: (i) entropies and (ii) distances in probability-space. In consequence, SCMs provide a simultaneous quantification of the randomness and the correlational structures present in the system under study. We address in this review important topics underlying the SCM structure, viz., (a) a good choice of probability metric space and (b) how to assess the best distance-choice, which in this context is called a “disequilibrium” and is denoted with the letter Q. Q, indeed the crucial SCM ingredient, is cast in terms of an associated distance D. Since out input data consists of time-series, we also discuss the best way of extracting from the time series a probability distribution P. As an illustration, we show just how these issues affect the description of the classical limit of quantum mechanics.
Publisher version (URL)http://dx.doi.org/10.3390/e13061055
Appears in Collections:(IFISC) Artículos
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