  The Mid-InfraRed Instrument (MIRI) on board the James Webb Space Telescope
(JWST) probes the chemistry and dust mineralogy of the inner regions of
protoplanetary disks. The observed spectra are unprecedented in their detail,
complicating interpretations which are mainly based on manual continuum
subtraction and 0D slab models. We investigate the physical conditions under
which the gas emits in protoplanetary disks. Based on MIRI spectra, we apply a
full Bayesian analysis that provides the posterior distributions of dust and
molecular properties. For doing so, we introduce the Dust Continuum Kit with
Line emission from Gas (DuCKLinG), a model describing the molecular line
emission and the dust continuum simultaneously without large computational
cost. The dust model is based on work by Juhasz et al. (2009, 2010). The
molecular emission is based on LTE slab models, but with radial gradients in
column densities and temperatures. The model is compared to observations using
Bayesian analysis. We benchmark this model to a complex thermo-chemical ProDiMo
model and fit the MIRI spectrum of GWLup. We find that the retrieved molecular
conditions from DuCKLinG fall within the true values from ProDiMo. The column
densities retrieved by Grant et al. (2023) fall within the retrieved ranges in
this study for all examined molecules (CO2, H2O, HCN, and C2H2). Similar
overlap is found for the temperatures with only the temperature range of HCN
not including the previously found value. This discrepancy may be due to the
simultaneous fitting of all molecules compared to the step-by-step fitting of
the previous study. There is statistically significant evidence for radial
temperature and column density gradients for H2O and CO2 compared to the
constant temperature and column density assumed in the 0D slab models.
Additionally, HCN and C2H2 emit from a small region with near constant
conditions.
