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001 978-3-030-38438-8
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020 _a9783030384388
_9978-3-030-38438-8
024 7 _a10.1007/978-3-030-38438-8
_2doi
050 4 _aQA273.A1-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aPanaretos, Victor M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 3 _aAn Invitation to Statistics in Wasserstein Space
_h[electronic resource] /
_cby Victor M. Panaretos, Yoav Zemel.
250 _a1st ed. 2020.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2020.
300 _aXIII, 147 p. 30 illus., 24 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs in Probability and Mathematical Statistics,
_x2365-4341
505 0 _aOptimal transportation -- The Wasserstein space -- Fréchet means in the Wasserstein space -- Phase variation and Fréchet means -- Construction of Fréchet means and multicouplings.
506 0 _aOpen Access
520 _aThis open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.
650 0 _aProbabilities.
650 1 4 _aProbability Theory.
700 1 _aZemel, Yoav.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030384371
776 0 8 _iPrinted edition:
_z9783030384395
830 0 _aSpringerBriefs in Probability and Mathematical Statistics,
_x2365-4341
856 4 0 _uhttps://doi.org/10.1007/978-3-030-38438-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-SOB
999 _c37736
_d37736