I have a comment on the example in Section 6 using distance (13). It seems to me that this shows a lack of consistency under lim eps->0 lim T->infty. However for any fixed finite T taking eps->0 recovers the true posterior. So I think this example would meet an alternative definition of consistency where the order of the limits is switched.

]]>Similarly, I would have thought a lot of summary statistics would converge to their limiting value almost surely, so in that case S1 could be weakened allowing S2 to be tightened, etc. ]]>