LEADER 04068nam 22007575 450 001 9910404119803321 005 20230125233546.0 010 $a3-030-38438-1 024 7 $a10.1007/978-3-030-38438-8 035 $a(CKB)4100000010770917 035 $a(DE-He213)978-3-030-38438-8 035 $a(MiAaPQ)EBC6135409 035 $a(Au-PeEL)EBL6135409 035 $a(OCoLC)1148226628 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/37237 035 $a(PPN)243227493 035 $a(EXLCZ)994100000010770917 100 $a20200310d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Invitation to Statistics in Wasserstein Space /$fby Victor M. Panaretos, Yoav Zemel 205 $a1st ed. 2020. 210 $aCham$cSpringer Nature$d2020 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XIII, 147 p. 30 illus., 24 illus. in color.) 225 1 $aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 311 $a3-030-38437-3 327 $aOptimal transportation -- The Wasserstein space -- Fréchet means in the Wasserstein space -- Phase variation and Fréchet means -- Construction of Fréchet means and multicouplings. 330 $aThis open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph. 410 0$aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4333 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 610 $aProbability Theory and Stochastic Processes 610 $aOptimal Transportation 610 $aMonge-Kantorovich Problem 610 $aBarycenter 610 $aMultimarginal Transport 610 $aFunctional Data Analysis 610 $aPoint Processes 610 $aRandom Measures 610 $aManifold Statistics 610 $aOpen Access 610 $aGeometrical statistics 610 $aWasserstein metric 610 $aFréchet mean 610 $aProcrustes analysis 610 $aPhase variation 610 $aGradient descent 610 $aProbability & statistics 610 $aStochastics 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 676 $a519.5 700 $aPanaretos$b Victor M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0742113 702 $aZemel$b Yoav$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910404119803321 996 $aAn Invitation to Statistics in Wasserstein Space$92259012 997 $aUNINA