Abstract
We propose an extension to Markov Chain Monte Carlo methods for inferences in the imprecise probability framework. The algorithm is based on simultaneous sampling from all the Markov chains targeting the distributions in the credal set. The algorithm constructs a chain of random sets, which can be used for conservative estimation of lower and upper expected values of derived random variables. Tight bounds on the set of estimators arising from the set of admitted stochastic models can be obtained when the credal set is finite for general models. Conservative bounds can be obtained for some classes of models also when the credal set is uncountable. Computational complexity for uncountable credal sets is not bounded, and heuristic fixes need to be implemented.
Supported by H2020-MSCA-ITN-2016 UTOPIAE, GA 722734.
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The project is: ERDF “A Research Platform focused on Industry 4.0 and Robotics in Ostrava Agglomeration”, No. CZ.02.1.01/0.0/0.0/17_049/0008425.
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Krpelik, D., Aslett, L.J.M., Coolen, F.P.A. (2021). Simultaneous Sampling for Robust Markov Chain Monte Carlo Inference. In: Vasile, M., Quagliarella, D. (eds) Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications. UQOP 2020. Space Technology Proceedings, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-030-80542-5_11
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DOI: https://doi.org/10.1007/978-3-030-80542-5_11
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