Bounds for the Distance Between the Distributions of Sums of Absolutely Continuous i.i.d. Convex-Ordered Random Variables with Applications

Christofides, Tasos C.; Vaggelatou, Eutichia

doi:10.1239/jap/1238592128

Cited by 1 publication

(1 citation statement)

References 13 publications

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“…If the probability function is nondecreasing, then total variation will provide the same solution as the Kolmogorov distance [23]. Furthermore, total variation is an upper bound on the Kolmogorov distance, i.e., D K ðP; QÞ D TV ðP; QÞ [20].…”

Section: Integral Probability Metricsmentioning

confidence: 99%

A Unifying Framework for Probabilistic Validation Metrics

Gardner

Lord

Barthorpe

2019

Journal of Verification, Validation and Uncertainty Quantification

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Probabilistic modeling methods are increasingly being employed in engineering applications. These approaches make inferences about the distribution for output quantities of interest. A challenge in applying probabilistic computer models (simulators) is validating output distributions against samples from observational data. An ideal validation metric is one that intuitively provides information on key differences between the simulator output and observational distributions, such as statistical distances/divergences. Within the literature, only a small set of statistical distances/divergences have been utilized for this task; often selected based on user experience and without reference to the wider variety available. As a result, this paper offers a unifying framework of statistical distances/divergences, categorizing those implemented within the literature, providing a greater understanding of their benefits, and offering new potential measures as validation metrics. In this paper, two families of measures for quantifying differences between distributions, that encompass the existing statistical distances/divergences within the literature, are analyzed: f-divergence and integral probability metrics (IPMs). Specific measures from these families are highlighted, providing an assessment of current and new validation metrics, with a discussion of their merits in determining simulator adequacy, offering validation metrics with greater sensitivity in quantifying differences across the range of probability mass.

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Section: Integral Probability Metricsmentioning

confidence: 99%