  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.
