  Searching for gravitational-wave signals is a challenging and computationally
intensive endeavor undertaken by multiple independent analysis pipelines. While
detection depends only on observed noisy data, it is sometimes inconsistently
defined in terms of source parameters that in reality are unknown, e.g., by
placing a threshold on the optimal signal-to-noise ratio (SNR). We present a
method to calibrate unphysical thresholds to search results by performing
Bayesian inference on real observations using a model that simultaneously
parametrizes the intrinsic network optimal SNR distribution and the effect of
search sensitivity on it. We find consistency with a fourth-order power law and
detection thresholds of $10.5_{-2.4}^{+2.1}$, $11.2_{-1.4}^{+1.2}$, and
$9.1_{-0.5}^{+0.5}$ (medians and $90\%$ credible intervals) for events with
false-alarm rates less than $1\,\mathrm{yr}^{-1}$ in the first, second, and
third LIGO-Virgo-KAGRA observing runs, respectively. Though event selection can
only be self-consistently reproduced by physical searches, employing our
inferred thresholds allows approximate observation-calibrated selection
criteria to be applied when efficiency is required and injection campaigns are
infeasible.
