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Keywords = generalized Phytagorean theorem

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22 pages, 357 KB  
Article
Exponential Families with External Parameters
by Marco Favretti
Entropy 2022, 24(5), 698; https://doi.org/10.3390/e24050698 - 14 May 2022
Cited by 2 | Viewed by 2333
Abstract
In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters. The main source for these statistical models resides in the Maximum Entropy framework where we have thermal parameters, corresponding to the natural [...] Read more.
In this paper we introduce a class of statistical models consisting of exponential families depending on additional parameters, called external parameters. The main source for these statistical models resides in the Maximum Entropy framework where we have thermal parameters, corresponding to the natural parameters of an exponential family, and mechanical parameters, here called external parameters. In the first part we we study the geometry of these models introducing a fibration of parameter space over external parameters. In the second part we investigate a class of evolution problems driven by a Fokker-Planck equation whose stationary distribution is an exponential family with external parameters. We discuss applications of these statistical models to thermodynamic length and isentropic evolution of thermodynamic systems and to a problem in the dynamic of quantitative traits in genetics. Full article
(This article belongs to the Collection Advances in Applied Statistical Mechanics)
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