This paper is episode four in the up-down instability series. We first figured out the instability exists (episode 1), then computed when binaries go after the instability (i.e. the endpoint, episode 2), and also checked binaries are really unstable in numerical relativity (episode 3). Now we look at the inference problem with LIGO/Virgo: if unstable up-down binaries enter the sensitivity window of the detector, will we be able to tell? We phrased the problem with some fancy stats using the so-called Savage Dickey density ratio, which is the right tool to answer this question. As is too often the case, current data are not informative enough but the future is bright and loud.