Title: Network Inference from a Link-Traced 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 link-traced
samples of that network. To do this, we first take summary statistics from an
observed link-traced network sample, such as a recruitment network of subjects
in a hard-to-reach 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 link-traced 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.