I feel safer in Jamaica than I did when walking around some towns/cities in the UK. As with living anywhere these days you have to be sensible. Walk around dripping with gold, wearing an expensive watch and under the weather from too much alcohol and you will be a target - just as you would anywhere in the world.
If you appear aloof and don't talk to others you will also be a target. However you can follow all of this advice and someone may still sidle up to you offering something, or someone of dubious value. Don't ignore them , just be polite and refuse the offer. Don't go through Jamaica living in a bubble or it may get popped sooner than you think, but that can happen anywhere in the world.