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• W2964046333 abstract "In this paper, we propose tight upper and lower bounds for the Wasserstein distance between any two univariate continuous distributions with probability densities $p_{1}$ and $p_{2}$ having nested supports. These explicit bounds are expressed in terms of the derivative of the likelihood ratio $p_{1}/p_{2}$ as well as the Stein kernel $tau_{1}$ of $p_{1}$. The method of proof relies on a new variant of Stein’s method which manipulates Stein operators. We give several applications of these bounds. Our main application is in Bayesian statistics: we derive explicit data-driven bounds on the Wasserstein distance between the posterior distribution based on a given prior and the no-prior posterior based uniquely on the sampling distribution. This is the first finite sample result confirming the well-known fact that with well-identified parameters and large sample sizes, reasonable choices of prior distributions will have only minor effects on posterior inferences if the data are benign." @default.
• W2964046333 created "2019-07-30" @default.
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• W2964046333 date "2017-02-01" @default.
• W2964046333 modified "2023-09-26" @default.
• W2964046333 title "Distances between nested densities and a measure of the impact of the prior in Bayesian statistics" @default.
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• W2964046333 doi "https://doi.org/10.1214/16-aap1202" @default.
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