  Online social networks (OSN) contain extensive amount of information about
the underlying society that is yet to be explored. One of the most feasible
technique to fetch information from OSN, crawling through Application
Programming Interface (API) requests, poses serious concerns over the the
guarantees of the estimates. In this work, we focus on making reliable
statistical inference with limited API crawls. Based on regenerative properties
of the random walks, we propose an unbiased estimator for the aggregated sum of
functions over edges and proved the connection between variance of the
estimator and spectral gap. In order to facilitate Bayesian inference on the
true value of the estimator, we derive the approximate posterior distribution
of the estimate. Later the proposed ideas are validated with numerical
experiments on inference problems in real-world networks.
