  The problem of measuring the true incremental effectiveness of a digital
advertising campaign is of increasing importance to marketers. With a large and
increasing percentage of digital advertising delivered via
Demand-Side-Platforms (DSPs) executing campaigns via Real-Time-Bidding (RTB)
auctions and programmatic approaches, a measurement solution that satisfies
both advertiser concerns and the constraints of a DSP is of particular
interest.
  MediaMath (a DSP) has developed the first practical, statistically sound
randomization-based methodology for causal ad effectiveness (or Ad Lift)
measurement by a DSP (or similar digital advertising execution system that may
not have full control over the advertising transaction mechanisms). We describe
our solution and establish its soundness within the causal framework of
counterfactuals and potential outcomes, and present a Gibbs-sampling procedure
for estimating confidence intervals around the estimated Ad Lift. We also
address practical complications (unique to the digital advertising setting)
that stem from the fact that digital advertising is targeted and measured via
identifiers (e.g., cookies, mobile advertising IDs) that may not be stable over
time. One such complication is the repeated occurrence of identifiers, leading
to interference among observations. Another is due to the possibility of
multiple identifiers being associated with the same consumer, leading to
"contamination" with some of their identifiers being assigned to the Treatment
group and others to the Control group. Complications such as these have
severely impaired previous efforts to derive accurate measurements of lift in
practice.
  In contrast to a few other papers on the subject, this paper has an
expository aim as well, and provides a rigorous, self-contained, and
readily-implementable treatment of all relevant concepts.
