Speaker
Description
Monte Carlo methods are among the most flexible tools for studying stochastic reaction networks, but they can be computationally expensive when exact simulation is used naively. In this talk, I will describe a general philosophy for improving such methods: exploit the structure inherent in the stochastic model itself. For reaction networks, that structure is often encoded through Poisson-process representations, such as Kurtz's random time change representation and related space-time Poisson constructions, which naturally suggest useful couplings between paths.
I will describe several simple but powerful coupling strategies, including the use of common Poisson processes, split couplings based on shared parts of reaction intensities, and shared space-time Poisson constructions. These couplings lead to efficient algorithms in a variety of settings, including parametric sensitivity analysis, multilevel Monte Carlo for expectations, and simulation of models with time-dependent intensities. The overall goal of the talk is introductory: to show how simple structural ideas can lead to substantial gains in efficiency across several Monte Carlo problems for stochastic reaction networks.
