Ensuring Reliable Monte Carlo Estimates of Network Properties

TL;DR

This paper develops and compares methods for assessing the reliability of Monte Carlo estimates in network sampling, addressing a gap in ensuring accurate network property estimation from partial data.

Contribution

It introduces multivariate MCMC output analysis techniques specifically tailored for network sampling, improving the assessment of estimate reliability in social network analysis.

Findings

Effective sample size and coverage probabilities are evaluated for different random walk algorithms.

The proposed methods provide computationally efficient tools for reliable network property estimation.

Comparison of simple and Metropolis-Hastings random walks highlights differences in estimation reliability.

Abstract

The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the network, access limitations, or the population of interest is hard to reach. In such cases, the application of random walk-based Markov chain Monte Carlo (MCMC) methods to estimate multiple network features is common. However, the reliability of these estimates has been largely ignored. We consider and further develop multivariate MCMC output analysis methods in the context of network sampling to directly address the reliability of the multivariate estimation. This approach yields principled, computationally efficient, and broadly applicable methods for assessing the Monte Carlo estimation procedure. In particular, with respect to two random-walk algorithms, a simple random walk and a Metropolis-Hastings random walk, we construct and compare network parameter estimates, effective sample sizes, coverage probabilities, and stopping rules, all of which speaks to the estimation reliability.