Applicazione della statistica inferenziale nei problemi di localizzazione della sorgente: un'analisi esplorativa dei processi stocastici su network

In recent years, one of the main challenges addressed in Complex Systems is the localization of the source of processes on networks. A medical-related example is the simulation of a simplified stochastic epileptic spread on a network of neurons, with the aim of finding the seeds of the dynamics (a single or more neurons responsible for its diffusion). For this purpose, Bayesian statistical inference, as a tool of statistical analysis, provides methods to deduce properties of an unknown probability distribution of a general process, given a certain number of samples. This helps the investigator in finding the most suitable initial condition given a consistent number of observations of the process. Two Statistical Physics approximation schemes for the solution of the presented Bayesian inference problem are proposed and compared. Moreover, message passing algorithms (especially Belief Propagation) are introduced as more accurate inference tools.