Exchangeable processes are extensively used in Bayesian nonparametrics to model exchangeable data. Most common approaches assign a law to the process through the specification of a random measure. When two processes only differ in the law of the random measure, a distance between random measures provides a natural way to compare them. In this work we propose one by relying on the Wasserstein distance. Moreover, we overcome the analytical difficulties of evaluating the distance by developing sharp upper and lower bounds. The specialization of these bounds to Gamma random measures provides the exact value of the Wasserstein distance in terms of the Kolmogorov distance between the base measures. The results are based on a forthcoming work in collaboration with A. Lijoi and I. Prunster.

Bayesian model comparison based on Wasserstein distances / Catalano, Marta; Lijoi, Antonio; Pruenster, Igor. - Smart Statistics for Smart Applications: Book of Short Papers SIS2019, (2019), pp. - (SIS 2019 Smart Statistics for Smart Applications, Università Cattolica del Sacro Cuore, Milano, June 18-21, 2019).

Bayesian model comparison based on Wasserstein distances

Marta Catalano;
2019

Abstract

Exchangeable processes are extensively used in Bayesian nonparametrics to model exchangeable data. Most common approaches assign a law to the process through the specification of a random measure. When two processes only differ in the law of the random measure, a distance between random measures provides a natural way to compare them. In this work we propose one by relying on the Wasserstein distance. Moreover, we overcome the analytical difficulties of evaluating the distance by developing sharp upper and lower bounds. The specialization of these bounds to Gamma random measures provides the exact value of the Wasserstein distance in terms of the Kolmogorov distance between the base measures. The results are based on a forthcoming work in collaboration with A. Lijoi and I. Prunster.
2019
9788891915108
Bayesian nonparametrics, Completely random measures, Increasing additive processes, Wasserstein distance
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11385/232222
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