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 $l_{CNM} = 12times 10^{-3}$. 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).
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