We investigate the asymptotic behavior of Bayesian posterior distributions
under independent and identically distributed ($i.i.d.$) misspecified models.
More specifically, we study the concentration of the posterior distribution on
neighborhoods of $f^{\star}$, the density that is closest in the
Kullback--Leibler sense to the true model $f_0$. We note, through examples, the
need for assumptions beyond the usual Kullback--Leibler support assumption. We
then investigate consistency with respect to a general metric under three
assumptions, each based on a notion of divergence measure, and then apply these
to a weighted $L_1$-metric in convex models and non-convex models. Although a
few results on this topic are available, we believe that these are somewhat
inaccessible due, in part, to the technicalities and the subtle differences
compared to the more familiar well-specified model case. One of our goals is to
make some of the available results, especially that of , more accessible.
Unlike their paper, our approach does not require construction of test
sequences. We also discuss a preliminary extension of the $i.i.d.$ results to
the independent but not identically distributed ($i.n.i.d.$) case.

研究误差模型下贝叶斯后验分布的渐近行为并研究多个假设，包括基于距离定义的偏差度量，以及应用于凸模型和非凸模型的加权 L1 度量，并探讨其扩展至不独立等但相互独立的情况。