| 期刊全称 | An Invitation to Statistics in Wasserstein Space | | 影响因子2023 | Victor M. Panaretos,Yoav Zemel | | 视频video | | | 发行地址 | Gives a succinct introduction to necessary mathematical background, focusing on the results useful for statistics from an otherwise vast mathematical literature.Presents an up-to-date overview of the | | 学科分类 | SpringerBriefs in Probability and Mathematical Statistics | | 图书封面 |  | | 影响因子 | .This 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 deformatio | | Pindex | Book‘‘‘‘‘‘‘‘ 2020 |
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发表于 2025-3-21 18:52:23
