Random Fields in Complex Systems Modelling: Information Geometry and Fisher Curves

Abstract

This poster intends to be a brief overview of random field models and information geometry basics in the study of stochastic complex systems. The focus is on how computational simulations can be performed in order to gain deeper undertanding about the underlying processes that govern these system's dynamics, by making use of the ubiquitous concept of information. In this context, both entropy and Fisher information are two statistical measures that play a fundamental role in this kind of analysis, provided there is a strong connection between them and the geometry of the random field models' parametric space. Throughout this overview, several subproblems that are part of the whole methodology are discussed, from parameter estimation in Markov random fields and Markov Chain Monte Carlo algorithms to the definition of the Fisher curves of the system. Experimental simulations are conducted in order to illustrate the described concepts and methods in a detailed and objective way.