I believe in ghosts, because I've seen them until about 5 or 6 years ago.
Don't see them anymore, sometimes I hear voices, but that could be anything.
I think saying that ghosts are not supported by science is stupid, mainly because we don't have a single clue what a ghost actually is.
Then how are you justified in saying that you believe in them? That's like saying "I believe in Gahanahoins, and I have no idea what they are".
And I agree with Automaton. The burden of proof is on the person making the claim, not those he is trying to convince. If I said "Fairies exist", then it wouldn't be your responsibility to prove that fairies don't exist, it would be mine.