Evaluating and Optimizing Network Sampling Designs: Decision Theory and Information Theory Perspectives

Abstract

Some of the most used sampling mechanisms that implicitly leverage a social network depend on tuning parameters; for instance, Respondent-Driven Sampling (RDS) is specified by the number of seeds and maximum number of referrals. We are interested in the problem of optimizing these sampling mechanisms with respect to their tuning parameters in order to optimize the inference on a population quantity, where such quantity is a function of the network and measurements taken at the nodes. This is done by formulating the problem in terms of decision theory and information theory, in turn. We discuss how the approaches discussed in this paper relate, via theoretical results, to other formalisms aimed to compare sampling designs, namely sufficiency and the Goel-DeGroot Criterion. The optimization procedure for different network sampling mechanisms is illustrated via simulations in the fashion of the ones used for Bayesian clinical trials.