The next meeting of the MAX team seminar will be on Tuesday, October 19. We will welcome Mirco Tribastone (IMT Lucca), for his talk entitled Reconciling discrete and continuous modeling for the analysis of large-scale Markov chains.
Abstract: Markov chains are a fundamental tool for stochastic modeling across a wide range of disciplines. Unfortunately, their exact analysis is often hindered in practice due to the massive size of the state space — an infamous problem plaguing many models based on a discrete state representation. When the system under study can be conveniently described as a population process, approximations based on mean-field theory have proved remarkably effective. However, since such approximations essentially disregard the effect of noise, they may potentially lead to inaccurate estimations under conditions such as bursty behavior, separation of populations into low- and high-abundance classes, and multi-stability. This talk will present a new analytical method that combines an accurate discrete representation of a subset of the state space with mean-field equations to improve accuracy at a user-tunable computational cost. Challenging examples drawn from queuing theory and systems biology will show how the method significantly outperforms state-of-the-art approximation methods.
This is joint work with Luca Bortolussi, Francesca Randone, Andrea Vandin, and Tabea Waizmann.