Network Science

Sampling networks from their posterior predictive distribution

RAVI GOYALa1, JOSEPH BLITZSTEINa2 and VICTOR DE GRUTTOLAa3

a1 Department of Biostatistics, Harvard School of Public Health, Boston, MA, 02115, USA (e-mail: rgoyal@hsph.harvard.edu)

a2 Department of Statistics, Harvard University, Cambridge, MA 02138-2901, USA (e-mail: blitzstein@stat.harvard.edu)

a3 Department of Biostatistics, Harvard School of Public Health, Boston, MA, 02115, USA (e-mail: degrut@hsph.harvard.edu)

Abstract

Recent research indicates that knowledge about social networks can be leveraged to increase efficiency of interventions (Valente, 2012). However, in many settings, there exists considerable uncertainty regarding the structure of the network. This can render the estimation of potential effects of network-based interventions difficult, as providing appropriate guidance to select interventions often requires a representation of the whole network. In order to make use of the network property estimates to simulate the effect of interventions, it may be beneficial to sample networks from an estimated posterior predictive distribution, which can be specified using a wide range of models. Sampling networks from a posterior predictive distribution of network properties ensures that the uncertainty about network property parameters is adequately captured. The tendency for relationships among network properties to exhibit sharp thresholds has important implications for understanding global network topology in the presence of uncertainty; therefore, it is essential to account for uncertainty. We provide detail needed to sample networks for the specific network properties of degree distribution, mixing frequency, and clustering. Our methods to generate networks are demonstrated using simulated data and data from the National Longitudinal Study of Adolescent Health.

Keywords:

  • network generation;
  • posterior predictive distribution;
  • network statistics
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