How can we explain psychic phenomena?

From: http://www.psiexplorer.com/theory.htm

To be precise, when we say that "X exists," we mean that the presently available, cumulative statistical database for experiments studying X, provides strong, scientifically credible evidence for repeatable, anomalous, X-like effects.

With this in mind, ESP exists, precognition exists, telepathy exists, and PK exists. ESP is statistically robust, meaning it can be reliably demonstrated through repeated trials, but it tends to be weak when simple geometric symbols are used as targets. Photographic or video targets often produce effects many times larger, and there is some evidence that ESP on natural locations (as opposed to photos of them), and in natural contexts, may be stronger yet.

Some PK effects have also been shown to exist. When individuals focus their intention on mechanical or electronic devices that fluctuate randomly, the fluctuations change in ways that conform to their mental intention. Under control conditions, when individuals direct their attention elsewhere, the fluctuations are in accordance with chance.

Note that we are using the terms ESP, telepathy and PK in the technical sense, not in the popular sense.

Opinions about mechanisms of psi are wide-ranging. Because the field is multidisciplinary, there are physical theories, psychological theories, psychophysical theories, sociological theories, and combinations of these.

On one end of the spectrum, the "physicalists" tend to believe that the "psi sensing capacity" is like any other human sensory system, and as such it will most likely be explained by known principles from biophysics, chemistry, and cognitive science. For these theorists, psi is expected to be accommodated into the existing scientific structure, with perhaps some modifications or extensions.

On the other end of the spectrum, the "mentalists" assert that reality would not exist if it were not for human consciousness. For these theorists, the nature of the universe is much more effervescent, thus accommodating psi into existing scientific models will require significant modification of science as we know it. Strong theoretical debates are common in parapsychology in part because spirit, religion, the meaning of life, and other philosophical conundrums commingle with quantum mechanics, probability theory, and neurons.

Some theorists have attempted to link psi phenomena with similar- sounding concepts from quantum mechanics, including non-locality, instantaneous correlations at a distance, and other anomalies. Such suggestions always spark vigorous debates, and at some point it seems the critics are inevitably accused of not properly understanding quantum mechanics.