  If damped Lyman alpha systems (DLAs) contain even modest amounts of dust, the
ultraviolet luminosity of the background quasar can be severely diminished.
When the spectrum is redshifted, this leads to a bias in optical surveys for
DLAs. Previous estimates of the magnitude of this effect are in some tension;
in particular, the distribution of DLAs in the column-density -- metallicity
plane has led to claims that we may be missing a considerable fraction of metal
rich, high column density DLAs, whereas radio surveys do not unveil a
substantial population of otherwise hidden systems. Motivated by this tension,
we perform a Bayesian parameter estimation analysis of a simple dust
obscuration model. We include radio and optical observations of DLAs in our
overall likelihood analysis and show that these do not, in fact, constitute
conflicting constraints.
  Our model gives statistical limits on the biasing effects of dust, predicting
that only 7% of DLAs are missing from optical samples due to dust obscuration;
at 2 sigma confidence, this figure takes a maximum value of 17%. This contrasts
with recent claims that DLA incidence rates are underestimated by 30 -- 50%.
Optical measures of the mean metallicities of DLAs are found to underestimate
the true value by just 0.1 dex (or at most 0.4 dex, 2 sigma confidence limit),
in agreement with the radio survey results of Akerman et al. The quantity most
affected by dust biasing is the total cosmic density of metals in DLAs,
Omega_{Z,DLA}, which is underestimated in optical surveys by a factor of
approximately two.
  (Abridged.)
