The Dependence of the $A_V$ Prior for SN\,Ia on Host Mass and Disk
  Inclination
  Supernovae type Ia (SNIa) are used as "standard candles" for cosmological
distance scales. To fit their light curve shape -- absolute luminosity
relation, one needs to assume an intrinsic color and a likelihood of host
galaxy extinction or a convolution of these, a color distribution prior. The
host galaxy extinction prior is typically assumed to be an exponential drop-off
for the current supernova programs ($P(A_V) \propto e^{-A_V/\tau_0}$). We
explore the validity of this prior using the distribution of extinction values
inferred when two galaxies accidentally overlap (an occulting galaxy pair). We
correct the supernova luminosity distances from the SDSS-III Supernova projects
(SDSS-SN) by matching the host galaxies to one of three templates from
occulting galaxy pairs based on the host galaxy mass and the $A_V$-bias -
prior-scale ($\tau_0$) relation from Jha et al. (2007).
  We find that introducing an $A_V$ prior that depends on host mass results in
lowered luminosity distances for the SDSS-SN on average but it does not reduce
the scatter in individual measurements. This points, in our view, to the need
for many more occulting galaxy templates to match to SNIa host galaxies to rule
out this possible source of scatter in the SNIa distance measurements. We match
occulting galaxy templates based on both mass and projected radius and we find
that one should match by stellar mass first with radius as a secondary
consideration. We discuss the caveats of the current approach and our aim is to
convince the reader that a library of occulting galaxy pairs observed with HST
will provide sufficient priors to improve (optical) SNIa measurements to the
next required accuracy in Cosmology.
