  We derive conditions for posterior consistency when the responses are
independent but not identically distributed ($i.n.i.d$) and the model is
"misspecified" to be a family of densities parametrized by a possibly infinite
dimensional parameter. Our approach has connections to key ideas developed for
$i.i.d$ models in Kleijn and van der Vaart(2006) and it's subsequent
simplification in Ramamoorthi, et al.(2014) (unpublished manuscript). While key
results in these two papers rely heavily on the convexity of the specified
family of densities, parametric families are seldom convex. In this note, we
take a direct approach to deriving posterior consistency with respect to
natural topologies on the parameter space without having to impose conditions
on the convex hull of the parametric family. We first derive our results for
the case when the responses are $i.i.d$ and then extend it to the $i.n.i.d$
case. As an example, we demonstrate the applicability of the results to the
Bayesian quantile estimation problem.
