There have been studies, but generally it is probably inference.
We can see brain activity, and different parts of the brain being stimulated. When we sleep, when we think, when we feel and so on.
I believe there is more proof of a subconscious, than there is of a telepathic mind link to an external source.
But yeah, this is all theory and conjecture.
For me it is inference because that is how it worked for me. I have dreamt of problems and woke up with solutions. The exact mechanism is unknown.