  Robust radiative transfer techniques are requisite for efficiently extracting
the physical and chemical information from molecular rotational lines.We study
several hypotheses that enable robust estimations of the column densities and
physical conditions when fitting one or two transitions per molecular species.
We study the extent to which simplifying assumptions aimed at reducing the
complexity of the problem introduce estimation biases and how to detect them.We
focus on the CO and HCO+ isotopologues and analyze maps of a 50 square
arcminutes field. We used the RADEX escape probability model to solve the
statistical equilibrium equations and compute the emerging line profiles,
assuming that all species coexist. Depending on the considered set of species,
we also fixed the abundance ratio between some species and explored different
values. We proposed a maximum likelihood estimator to infer the physical
conditions and considered the effect of both the thermal noise and calibration
uncertainty. We analyzed any potential biases induced by model
misspecifications by comparing the results on the actual data for several sets
of species and confirmed with Monte Carlo simulations. The variance of the
estimations and the efficiency of the estimator were studied based on the
Cram{\'e}r-Rao lower bound.Column densities can be estimated with 30% accuracy,
while the best estimations of the volume density are found to be within a
factor of two. Under the chosen model framework, the peak 12CO(1--0) is useful
for constraining the kinetic temperature. The thermal pressure is better and
more robustly estimated than the volume density and kinetic temperature
separately. Analyzing CO and HCO+ isotopologues and fitting the full line
profile are recommended practices with respect to detecting possible
biases.Combining a non-local thermodynamic equilibrium model with a rigorous
analysis of the accuracy allows us to obtain an efficient estimator and
identify where the model is misspecified. We note that other combinations of
molecular lines could be studied in the future.
