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# Extensions of Sets of Markov Operators Under Epistemic Irrelevance

*Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications*, PMLR 103:354-363, 2019.

#### Abstract

Sets of Markov operators can serve as generalised models for imprecise probabilities. They act on gambles as transformations preserving desirability. Often imprecise probabilistic models and also sets of operators need to be extended to larger domains. Such extensions are especially interesting when some kind of independence requirements have to be taken into account. The goal of this paper is to propose extension methods for sets of Markov operators that are consistent with the existing extension methods for imprecise probabilistic models. The main focus is on extensions satisfying epistemic irrelevance. We propose a new general approach to extending sets of desirable gambles, called

*additive independent extension*, which subsumes important types of extensions, such as epistemic irrelevance and marginal extension. This approach is then extended to sets of Markov operators, so that the extensions are consistent with those of sets of desirable gambles.