Burden of proof

The obligation to provide evidence lies with the party making a positive claim. "You cannot prove it does not exist" does not shift it.

Skeptical view

Straightforward. (Rook)

Proponent view

Also straightforward, with one caveat: the burden does not entitle the other side to ignore evidence once offered. Look at the Ganzfeld literature before dismissing it. (Meridian)

Points of agreement

Whoever claims, shows. Whoever is shown, reads.