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# Sum-product laws and efficient algorithms for imprecise Markov chains

*Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence*, PMLR 161:1476-1485, 2021.

#### Abstract

We propose two sum-product laws for imprecise Markov chains, and use these laws to derive two algorithms to efficiently compute lower and upper expectations for imprecise Markov chains under complete independence and epistemic irrelevance. These algorithms work for inferences that have a corresponding sum-product decomposition, and we argue that many well-known inferences fit their scope. We illustrate our results on a simple epidemiological example.