Extensions of Sets of Markov Operators Under Epistemic Irrelevance

Damjan Skulj
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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v103-skulj19a, title = {Extensions of Sets of Markov Operators Under Epistemic Irrelevance}, author = {Skulj, Damjan}, booktitle = {Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {354--363}, year = {2019}, editor = {De Bock, Jasper and de Campos, Cassio P. and de Cooman, Gert and Quaeghebeur, Erik and Wheeler, Gregory}, volume = {103}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v103/skulj19a/skulj19a.pdf}, url = {http://proceedings.mlr.press/v103/skulj19a.html}, 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.} }
Endnote
%0 Conference Paper %T Extensions of Sets of Markov Operators Under Epistemic Irrelevance %A Damjan Skulj %B Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2019 %E Jasper De Bock %E Cassio P. de Campos %E Gert de Cooman %E Erik Quaeghebeur %E Gregory Wheeler %F pmlr-v103-skulj19a %I PMLR %P 354--363 %U http://proceedings.mlr.press/v103/skulj19a.html %V 103 %X 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.
APA
Skulj, D.. (2019). Extensions of Sets of Markov Operators Under Epistemic Irrelevance. Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 103:354-363 Available from http://proceedings.mlr.press/v103/skulj19a.html.

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