  We present a generalized analytical Bayesian framework for calculating the
occurrence rate of steady emission (or absorption) in astrophysical objects. As
a proof-of-concept, we apply this framework to non-flaring quiescent radio
emission in ultracool ($\leq$ M7) dwarfs. Using simulations, we show that our
framework recovers the simulated radio occurrence rate to within 1-5% for
sample sizes of 10-100 objects when averaged over an ensemble of trials and
simulated occurrence rates for our assumed luminosity distribution models. In
contrast, existing detection rate studies may under-predict the simulated rate
by 51-66% because of sensitivity limits. Using all available literature results
for samples of 82 ultracool M dwarfs, 74 L dwarfs, and 23 T/Y dwarfs, we find
that the maximum-likelihood quiescent radio occurrence rate is between
$15^{+4}_{-4}$ - $20^{+6}_{-5}$%, depending on the luminosity prior that we
assume. Comparing each spectral type, we find occurrence rates of
$17^{+9}_{-7}$ - $25^{+13}_{-10}$% for M dwarfs, $10^{+5}_{-4}$ -
$13^{+7}_{-5}$% for L dwarfs, and $23^{+11}_{-9}$ - $29^{+13}_{-11}$% for T/Y
dwarfs. We rule out potential selection effects and speculate that age and/or
rotation may account for tentative evidence that the quiescent radio occurrence
rate of L dwarfs may be suppressed compared to M and T/Y dwarfs and phenomenon.
Finally, we discuss how we can harness our occurrence rate framework to
carefully assess the possible physics that may be contributing to observed
occurrence rate trends.
