2013/12/31 by Siva Athreya, Adrian Röllin · 3 citations
Mathematics · Medicine · #Ergodic theory #Graph #HIV, Drug Use, Sexual Risk #Invariant (physics) #Invariant measure #Limiting #Markov Chains and Monte Carlo Methods #Sampling (signal processing) #Survey Sampling and Estimation Techniques #Transformation (genetics) #math.PR #math.ST #stat.TH
paper · pdf · doi:10.1214/15-aap1144
published in The Annals of Applied Probability 26(4) (Institute of Mathematical Statistics) · Published at http://dx.doi.org/10.1214/15-AAP1144 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex created_date 2016/06/24 · openalex publication_date 2016/08/01 · arxiv created 2016/09/28 · arxiv updated 2016/09/29 · openalex updated_date 2026/08/05
We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related to the invariant measure of the ergodic sequence. For specific sampling procedures, we describe the transformation explicitly.