Abstraction-Guided Truncations for Stationary Distributions of Markov Population Models
This method addresses the challenge of long-run behavior analysis in Markov models for researchers in computational biology or systems modeling, but it appears incremental as it builds on existing truncation and lumping techniques.
The authors tackled the problem of computing stationary distributions for Markov population models by proposing a truncation-based approximation that uses state-space lumping and iterative refinement to learn a tailored finite-state projection, demonstrating applicability to non-linear problems with complex stationary behaviors.
To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection tailored to the stationary behavior. We demonstrate the method's applicability to a wide range of non-linear problems with complex stationary behaviors.