Let's Recall the Words of Willie Sutton
When the prolific gentleman bank thief, Willie Sutton, was asked why he chose to rob banks, he is generally said to have replied, "Because that's where the money is". So it seems like no brainer that expats - the most middle class of whom appear as (and are) extremely wealthy compared to a majority of Dominicans, are singled out by thieves.
I agree with Quaqualita's statement in an earlier post that, unlike days gone by, what we are facing now in Costa Azul and other similar expat enclaves are gangs of professional thieves who are connected to the police to the extent that they have immunity from serious efforts at apprehension and punishment. By definition this kind of criminal is does not give a flip about who's a nice Dominican people loving, Spanish speaking, expat and who is only here to enjoy the beauty of this island at bargian cost and hopes to see as little of the local people as possible (except perhaps the underage prosties).
Talk about ostentation (and other cultural sensitivity drivel) is meaningless in this context. I suspect that the only reason that the neighborhoods of rich Dominicans that are sometimes also shared by some expats (you know, like the ones right in Puerto Plata that have the regular city streets blocked off to through traffic by a guardhouses) and which look pretty "ostentatious" to me, may be suffering little or less of this kind of crime because it is known far and wide that the people living in there are politically connected in such a way that the usual impunity enjoyed by these gangs will not apply.