Inferenza Statistica nei Modelli ad Agenti: applicazioni a modelli Preda-Predatore

Agent-Based Models (ABMs) are among the most insightful frameworks for the study of Complex Systems in various fields of knowledge. They are simple to understand and allow to describe complicated emergent phenomena as a consequence of simpler interaction rules between elementary entities called agents. There is a trade off to their use, though: their parameters are difficult to calibrate and the estimation of latent variables is usually a neglected task, further limiting their potential as modelling and predictive tools for systems that have been, so far, too challenging to tackle effectively with other modelling frameworks. In this work, we showcase how to cast parameter calibration as a statistical inference problem, using as a case study the Predator-Prey model, one of the most studied ABMs. The approach we use starts by applying a translation protocol to transform an Agent-Based Model to a Probabilistic Graphical Model (PGM). Through this process, the Agent Based Model becomes learnable, meaning that it is capable to be informed by data in a principled way, as a tractable Likelihood function can be defined and used as an objective function to minimize, transforming the estimation problem into an optimization one. This process is able to estimate not only the parameters, but also any other latent variable, as long as enough data is available. We test the Likelihood-based estimation approach in two different scenarios of increased complexity, that result in two different Probabilistic Graphical Models. In the simplest case, the model is provided with full information about the system, whereas in the second case the model is given only limited, partial data about the state of the system; in both scenarios the goal is to perform statistical inference from the available data to provide an estimate of the real parameters that generated it. The results we obtain from the learning process are mixed: in the former case, the parameters are correctly estimated with better accuracy as more in formation is provided to the model; in the latter, the high dimensionality of the problem coupled with the limited and noisy data available impacts negatively the quality of estimation, underscoring the importance of having access to more, robust data as the calibration task difficulty increases.