Particle Filters and Factor Graphs for Narrative Space: A Compositional Framework for Scenario Analysis
We develop a formal framework for scenario-based analysis in which narratives—structured accounts of how a situation might evolve—are treated as hidden Markov models whose latent states are explored via particle filters. The framework, introduced in an earlier paper for television series architecture, extends naturally to real-world scenario analysis: geopolitical, technological, and financial narratives whose state spaces interact. When multiple narratives are analyzed independently, their interdependencies remain implicit. We show that these dependencies can be made explicit using factor graphs, and that the resulting compositional structure has a natural interpretation in the language of decorated cospans and operads. The category- theoretic formalization is not ornamental: it provides the algebra for composing open narrative systems along shared interfaces, and it scales to the many-narrative setting that real-world scenario analysis requires. We illustrate with the push to democratise private markets—four interacting narratives whose factor graph reveals a self-reinforcing loop that is also, traced in the other direction, a self-destructing one—and interpret their factor graph as a colimit in a category of open systems.