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Equivalence of weak and strong modes of measures on topological vector spaces
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Lie, Han Cheng and Sullivan, T. J. (2018) Equivalence of weak and strong modes of measures on topological vector spaces. Inverse Problems, 34 (11). 115013. doi:10.1088/1361-6420/aadef2 ISSN 0266-5611.
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WRAP-Equivalence-weak-strong-modes-measures-topological-spaces-Sullivan-2018.pdf - Accepted Version - Requires a PDF viewer. Download (756Kb) | Preview |
Official URL: http://dx.doi.org/10.1088/1361-6420/aadef2
Abstract
A strong mode of a probability measure on a normed space X can be defined as a point u such that the mass of the ball centred at u uniformly dominates the mass of all other balls in the small-radius limit. Helin and Burger weakened this definition by considering only pairwise comparisons with balls whose centres differ by vectors in a dense, proper linear subspace E of X, and posed the question of when these two types of modes coincide. We show that, in a more general setting of metrisable vector spaces equipped with measures that are finite on bounded sets, the density of E and a uniformity condition suffice for the equivalence of these two types of modes. We accomplish this by introducing a new, intermediate type of mode. We also show that these modes can be inequivalent if the uniformity condition fails. Our results shed light on the relationships between among various notions of maximum a posteriori estimator in non-parametric Bayesian inference.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics T Technology > T Technology (General) |
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering Faculty of Science, Engineering and Medicine > Science > Mathematics |
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Library of Congress Subject Headings (LCSH): | Probabilities, Linear topological spaces, Analysis of covariance | |||||||||
Journal or Publication Title: | Inverse Problems | |||||||||
Publisher: | Institute of Physics Publishing Ltd. | |||||||||
ISSN: | 0266-5611 | |||||||||
Official Date: | 1 November 2018 | |||||||||
Dates: |
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Volume: | 34 | |||||||||
Number: | 11 | |||||||||
Article Number: | 115013 | |||||||||
DOI: | 10.1088/1361-6420/aadef2 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Reuse Statement (publisher, data, author rights): | "This is an author-created, un-copyedited version of an article accepted for publication/published in Inverse Problems. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1361-6420/aadef2 | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Copyright Holders: | © 2018 IOP Publishing Ltd | |||||||||
Date of first compliant deposit: | 15 April 2020 | |||||||||
Date of first compliant Open Access: | 15 April 2020 | |||||||||
RIOXX Funder/Project Grant: |
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