I have had items stolen on the Island.
(good thing my stuff is of little value)
The nice thing about A/C is that people here are not all that impressed by "luxury items", so there is no need to bring them.
Very casual here, so leave the Rolex at home, and it's one less worry.
If you rent a golf car, NEVER leave anything in it; and always lock it up.
Petty crime is VERY common Here.
They are mostly "crimes of opportunity" - so try not to give anyone an "opportunity".
A Hotel security guard can not be everyplace at once, and if you come home late, you may find him napping in your golf cart!
So use your good travel-judgement.
Take extra care on the mainland, There is more crime there.
Have Fun!