An improved estimator of Shannon entropy with applications to systems with memory

Many systems can be described with Markovian models in which the future state of the system only depends on its present state. While in some cases this is enough to predict the evolution of the system, in other cases it is necessary to take into account also the past states of the system. Which is the minimum number of past states needed in order to faithfully predict the future state of the system? It turns out that a simple answer to this question can be found from an analysis of Shannon entropy. Much work has been devoted in the past to obtain an accurate estimator of Shannon entropy for data coming from small samples. In this talk I will present an entropy estimator that takes into account time correlations and is particular useful to study systems with memory. As an example I will apply this method to the determination of the minimum memory required to describe lexical statistics of texts in different languages and daily precipitations in different worldwide locations.

Hybrid format: seminar room and Zoom link below.

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David Sánchez

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