  We present a statistical model of the selection function of cold neutral gas
in high-redshift (z~2.5) absorption systems. The model is based on the
canonical two-phase model of the neutral gas in the interstellar medium and
contains only one parameter for which we do not have direct observational
priors: namely the central pressure (P*) of an L* halo at z=2.5. Using
observations of the fraction of cold gas absorption in strong HI-selected
absorbers, we are able to constrain P*. The model simultaneously reproduces the
column density distributions of HI and H$_2$, and we derive an expected total
incidence of cold gas at z~2.5 of $l_{CNM} = 12\times 10^{-3}$. Compared to
recent measurements of the incidence of CI-selected absorbers (EW$_{CI\,1560}$
> 0.4 {\AA}), the value of $l_{CNM}$ from our model indicates that only ~15% of
the total cold gas would lead to strong CI absorption (EW > 0.4 {\AA}).
Nevertheless, CI lines are extremely useful probes of the cold gas as they are
relatively easy to detect and provide direct constraints on the physical
conditions. Lastly, our model self-consistently reproduces the fraction of cold
gas absorbers as a function of N(HI).
