Network Inference from a LinkTraced Sample using Approximate Bayesian Computation
Abstract
We present a new inference method based on approximate Bayesian computation for estimating parameters governing an entire network based on linktraced samples of that network. To do this, we first take summary statistics from an observed linktraced network sample, such as a recruitment network of subjects in a hardtoreach population. Then we assume prior distributions, such as multivariate uniform, for the distribution of some parameters governing the structure of the network and behaviour of its nodes. Then, we draw many independent and identically distributed values for these parameters. For each set of values, we simulate a population network, take a linktraced sample from that network, and find the summary statistics for that sample. The statistics from the sample, and the parameters that eventually led to that sample, are collectively treated as a single point. We take a Kernel Density estimate of the points from many simulations, and observe the density across the hyperplane coinciding with the statistic values of the originally observed sample. This density function is treat as a posterior estimate of the paramaters of the network that provided the observed sample. We also apply this method to a network of precedence citations between legal documents, centered around cases overseen by the Supreme Court of Canada, is observed. The features of certain cases that lead to their frequent citation are inferred, and their effects estimated by ABC. Future work and extensions are also briefly discussed.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.03861
 Bibcode:
 2017arXiv170103861D
 Keywords:

 Statistics  Computation;
 Computer Science  Social and Information Networks;
 Physics  Physics and Society
 EPrint:
 35 pages, 9 figures