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    Local dependence in random graph models: characterization, properties and statistical inference

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    Author
    Schweinberger, Michael; Handcock, Mark S.
    Date
    2015
    Abstract
    Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’.
    Citation
    Schweinberger, Michael and Handcock, Mark S.. "Local dependence in random graph models: characterization, properties and statistical inference." Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77, no. 3 (2015) Wiley: 647-676. https://doi.org/10.1111/rssb.12081.
    Published Version
    https://doi.org/10.1111/rssb.12081
    Keyword
    Exponential families; Local dependence; M-dependence; Model degeneracy; Social networks; More... Weak dependence Less...
    Type
    Journal article
    Publisher
    Wiley
    Citable link to this page
    https://hdl.handle.net/1911/94849
    Rights
    This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Wiley.
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    • Faculty Publications [4988]
    • Statistics Publications [137]

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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map