Publikation
Analysis of Markov jump processes under terminal constraints
Michael Backenköhler; Luca Bortolussi; Gerrit Großmann; Verena Wolf
In: Jan Friso Groote; Kim Guldstrand Larsen; (Hrsg.). Tools and Algorithms for the Construction and Analysis of Systems. International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS-2021), 27th International Conference, TACAS 2021, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021, March 27 - April 1, Luxembourg City, Luxembourg, Pages 210-229, Vol. 12651, ISBN 978-3-030-72016-2, Springer, Switzerland, 3/2021.
Zusammenfassung
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging 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 yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method’s applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.