When we compare data-based perceptions with others, which confirm or correlate with our defined perceptions.
This extends to e.g. two simultaneous out-of-body experiencers, who are assigned to a similar target, double-blind, and who report statistically significant correlated data (in real time). This has been done at various institutes (Monroe Institute, for one).
Similarly, the resurrection of Jesus or the host of Light at Garabandal (also filmed) would be in this category of reliable sense data.
The recording of such events on video or with other measures also gives high credibility, in a second degree.
A third area of verification is replicability, the control at least of matter by protocols.
http://www.tiller.org has interesting information about human intention and their psi fields' ability to influence quantum states. This provides a direct causation regarding psi.