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Hamiltonian truncation of the shallow water equation (1994)

Zhong, Ge ; Scovel, Clint

Springer

Letters in mathematical physics 31 (1994), S. 1-13

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ISSN: 1573-0530

Schlagwort(e): 73D20 ; 35Q35 ; 76B15 ; 65P05 ; 53C80 ; 70H99

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik , Physik

Notizen: Abstract In this Letter, we describe a truncation of the Eulerian description of the shallow water equation of climate modeling to a finite-dimensional Hamiltonian system. The technique is to use an isomorphism from a semidirect product Poisson manifold to a direct product of Poisson manifolds, both of whose components are truncatable to finite-dimensional Poisson manifolds, based on Moser's theorem on volume elements.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00751167

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On the Brittleness of Bayesian Inference (2015)

Owhadi, Houman ; Scovel, Clint ; Sullivan, T. J.

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Publikationsdatum: 2021-10-28

Beschreibung: With the advent of high-performance computing, Bayesian methods are becoming increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods can impact the making of sometimes critical decisions in increasingly complicated contexts, the sensitivity of their posterior conclusions with respect to the underlying models and prior beliefs is a pressing question to which there currently exist positive and negative answers. We report new results suggesting that, although Bayesian methods are robust when the number of possible outcomes is finite or when only a finite number of marginals of the data-generating distribution are unknown, they could be generically brittle when applied to continuous systems (and their discretizations) with finite information on the data-generating distribution. If closeness is defined in terms of the total variation (TV) metric or the matching of a finite system of generalized moments, then (1) two practitioners who use arbitrarily close models and observe the same (possibly arbitrarily large amount of) data may reach opposite conclusions; and (2) any given prior and model can be slightly perturbed to achieve any desired posterior conclusion. The mechanism causing brittleness/robustness suggests that learning and robustness are antagonistic requirements, which raises the possibility of a missing stability condition when using Bayesian inference in a continuous world under finite information.

Sprache: Englisch

Materialart: article , doc-type:article

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