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2020 Stability of doubly-intractable distributions
Michael Habeck, Daniel Rudolf, Björn Sprungk
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP341

Abstract

Doubly-intractable distributions appear naturally as posterior distributions in Bayesian inference frameworks whenever the likelihood contains a normalizing function $Z$. Having two such functions $Z$ and $\widetilde Z$ we provide estimates of the total variation and $1$-Wasserstein distance of the resulting posterior probability measures. As a consequence this leads to local Lipschitz continuity w.r.t. $Z$. In the more general framework of a random function $\widetilde Z$ we derive bounds on the expected total variation and expected $1$-Wasserstein distance. The applicability of the estimates is illustrated within the setting of two representative Monte Carlo recovery scenarios.

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Michael Habeck. Daniel Rudolf. Björn Sprungk. "Stability of doubly-intractable distributions." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP341

Information

Received: 3 May 2020; Accepted: 12 August 2020; Published: 2020
First available in Project Euclid: 8 September 2020

zbMATH: 1448.60009
Digital Object Identifier: 10.1214/20-ECP341

Subjects:
Primary: 60B10, 62C10, 65C05

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