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Advances in Probability and Mathematical StatisticsTransport Distances on Random Vectors of Measures: Recent Advances in Bayesian Nonparametrics

Advances in Probability and Mathematical Statistics: Transport Distances on Random Vectors of... [Random vectors of measures are at the core of many recent developments in Bayesian nonparametrics. For a deep understanding of these infinite-dimensional discrete random structures and their impact on the inferential and theoretical properties of the induced models, we consider a class of transport distances based on the Wasserstein distance. The geometrical definition makes it ideal for measuring similarity between distributions with possibly different supports. Moreover, when applied to random vectors of measures with independent increments (completely random vectors), the interesting theoretical properties are coupled with analytical tractability. This leads to a new measure of dependence for completely random vectors and the quantification of the impact of hyperparameters in notable models for exchangeable time-to-event data.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Advances in Probability and Mathematical StatisticsTransport Distances on Random Vectors of Measures: Recent Advances in Bayesian Nonparametrics

Part of the Progress in Probability Book Series (volume 79)
Editors: Hernández‐Hernández, Daniel; Leonardi, Florencia; Mena, Ramsés H.; Pardo Millán, Juan Carlos
Catalano, Marta; Lijoi, Antonio; Prünster, Igor
Advances in Probability and Mathematical Statistics — Aug 5, 2021
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References (8)

Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-85324-2
Pages
59 –70
DOI
10.1007/978-3-030-85325-9_4
Publisher site
See Chapter on Publisher Site

Abstract

[Random vectors of measures are at the core of many recent developments in Bayesian nonparametrics. For a deep understanding of these infinite-dimensional discrete random structures and their impact on the inferential and theoretical properties of the induced models, we consider a class of transport distances based on the Wasserstein distance. The geometrical definition makes it ideal for measuring similarity between distributions with possibly different supports. Moreover, when applied to random vectors of measures with independent increments (completely random vectors), the interesting theoretical properties are coupled with analytical tractability. This leads to a new measure of dependence for completely random vectors and the quantification of the impact of hyperparameters in notable models for exchangeable time-to-event data.]

Published: Aug 5, 2021

Keywords: Bayesian nonparametrics; Completely random measures; Completely random vectors; Compound Poisson approximation; Dependence; Lévy copula; Partial exchangeability; Wasserstein distance

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