  There is a growing need for machine learning-based anomaly detection
strategies to broaden the search for Beyond-the-Standard-Model (BSM) physics at
the Large Hadron Collider (LHC) and elsewhere. The first step of any anomaly
detection approach is to specify observables and then use them to decide on a
set of anomalous events. One common choice is to select events that have low
probability density. It is a well-known fact that probability densities are not
invariant under coordinate transformations, so the sensitivity can depend on
the initial choice of coordinates. The broader machine learning community has
recently connected coordinate sensitivity with anomaly detection and our goal
is to bring awareness of this issue to the growing high energy physics
literature on anomaly detection. In addition to analytical explanations, we
provide numerical examples from simple random variables and from the LHC
Olympics Dataset that show how using probability density as an anomaly score
can lead to events being classified as anomalous or not depending on the
coordinate frame.
