  With the increasing use of neural networks in critical systems, runtime
monitoring becomes essential to reject unsafe predictions during inference.
Various techniques have emerged to establish rejection scores that maximize the
separability between the distributions of safe and unsafe predictions. The
efficacy of these approaches is mostly evaluated using threshold-agnostic
metrics, such as the area under the receiver operating characteristic curve.
However, in real-world applications, an effective monitor also requires
identifying a good threshold to transform these scores into meaningful binary
decisions. Despite the pivotal importance of threshold optimization, this
problem has received little attention. A few studies touch upon this question,
but they typically assume that the runtime data distribution mirrors the
training distribution, which is a strong assumption as monitors are supposed to
safeguard a system against potentially unforeseen threats. In this work, we
present rigorous experiments on various image datasets to investigate: 1. The
effectiveness of monitors in handling unforeseen threats, which are not
available during threshold adjustments. 2. Whether integrating generic threats
into the threshold optimization scheme can enhance the robustness of monitors.
