  Several different methods are regularly used to infer the properties of the
neutral interstellar medium (ISM) using atomic hydrogen (H I) 21cm absorption
and emission spectra. In this work, we study various techniques used for
inferring ISM gas phase properties, namely the correlation between brightness
temperature and optical depth $(T_B(v)$, $\tau(v))$ at each channel velocity
($v$), and decomposition into Gaussian components, by creating mock spectra
from a 3D magnetohydrodynamic simulation of a two-phase, turbulent ISM. We
propose a physically motivated model to explain the $T_B(v)-\tau(v)$
distribution and relate the model parameters to properties like warm gas spin
temperature and cold cloud length scales. Two methods based on Gaussian
decomposition -- using only absorption spectra and both absorption and emission
spectra -- are used to infer the column density distribution as a function of
temperature. In observations, such analysis reveals the puzzle of large amounts
(significantly higher than in simulations) of gas with temperature in the
thermally unstable range of $\sim$200 K to $\sim$2000 K and a lack of the
expected bimodal (two-phase) temperature distribution. We show that, in
simulation, both methods are able to recover the actual gas distribution in the
simulation till temperatures $\lesssim2500$~K (and the two-phase distribution
in general) reasonably well. We find our results to be robust to a range of
effects such as noise, varying emission beam size, and simulation resolution.
This shows that the observational inferences are unlikely to be artifacts, thus
highlighting a tension between observations and simulations. We discuss
possible reasons for this tension and ways to resolve it.
