Analysis of Markov Jump Processes under Terminal Constraints

TL;DR

This paper introduces a novel state-space lumping method for Markov jump processes that efficiently computes system behavior under terminal constraints, applicable to Bayesian inference and rare event analysis.

Contribution

It presents a new approximate bridging distribution technique using state-space lumping for Markov jump processes with guaranteed bounds under endpoint constraints.

Findings

Provides a finite-state projection with guaranteed lower bounds.

Applicable to Bayesian inference and rare event analysis.

Demonstrates effectiveness on diverse problems.

Abstract

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.