Journal Article

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

Schweinberger, Michael, Handcock, Mark S.

2015

Overview

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’.

• Publisher: Royal Statistical Society,Blackwell Publishing Ltd,John Wiley & Sons Ltd,Oxford University Press
• Subject: Bayesian analysis / Bayesian method / Economic analysis / Exponential families / Families & family life / Graph theory / Inference / Local dependence / M-dependence / Markov chains / Markov models / Methodology / Model degeneracy / Neighborhoods / Predictive modeling / Property / Simulation / Social networks / Spatial models / Statistical analysis / Statistical graphs / Statistical inference / Statistical inferences / Statistical methods / Statistics / Stochastic models / Studies / Terrorism / Terrorists / Time / Time series / time series analysis / Truth / Uncertainty / Weak dependence