  We study how the amount of correlation between observations collected by
distinct sensors/learners affects data collection and collaboration strategies
by analyzing Fisher information and the Cramer-Rao bound. In particular, we
consider a simple setting wherein two sensors sample from a bivariate Gaussian
distribution, which already motivates the adoption of various strategies,
depending on the correlation between the two variables and resource
constraints. We identify two particular scenarios: (1) where the knowledge of
the correlation between samples cannot be leveraged for collaborative
estimation purposes and (2) where the optimal data collection strategy involves
investing scarce resources to collaboratively sample and transfer information
that is not of immediate interest and whose statistics are already known, with
the sole goal of increasing the confidence on an estimate of the parameter of
interest. We discuss two applications, IoT DDoS attack detection and
distributed estimation in wireless sensor networks, that may benefit from our
results.
