  A growing body of literature attempts to learn about contagion using
observational (i.e. non-experimental) data collected from a single social
network. While the conclusions of these studies may be correct, the methods
rely on assumptions that are likely--and sometimes guaranteed to be--false, and
therefore the evidence for the conclusions is often weaker than it seems.
Developing methods that do not need to rely on implausible assumptions is an
incredibly challenging and important open problem in statistics. Appropriate
methods don't (yet!) exist, so researchers hoping to learn about contagion from
observational social network data are sometimes faced with a dilemma: they can
abandon their research program, or they can use inappropriate methods. This
chapter will focus on the challenges and the open problems and will not weigh
in on that dilemma, except to mention here that the most responsible way to use
any statistical method, especially when it is well-known that the assumptions
on which it rests do not hold, is with a healthy dose of skepticism, with
honest acknowledgment and deep understanding of the limitations, and with
copious caveats about how to interpret the results.
