Yesterday, I linked to a discussion between two New Testament scholars about the historicity of miracles. Some of the cases they discussed involve people who weren't expecting to witness a miracle or were even predisposed to not see one occur. Those cases are significant in light of the common skeptical objection that prior expectation makes people more likely to think something happened that didn't actually happen. The objection is framed differently in different contexts. Sometimes it will be expressed in terms of bias. Biased witnesses are less reliable. Or the objection is raised in the context of hallucinations. People hallucinate what they expect to see. Whatever form the objection takes, arguments like those are common. And some of the cases Michael Licona and Craig Keener address in the interview I discussed yesterday are insusceptible to that objection to some extent.
Two of the most prominent leaders of early Christianity, James and Paul, seem to have been unbelievers when they purportedly saw the risen Jesus. (On James, see here. On Paul, see here.) For that and many other reasons, the skeptical objection I've referred to above doesn't carry much weight as an argument against Christianity.
Concerning the paranormal in general, not just in the context of Christianity, here are some other examples:
"Those séances [involving Eusapia Palladino] led to the publication of a massive, graphically detailed account of eleven sessions with Eusapia, conducted by three very experienced researchers. That report describes, play by play, what happened during the séances, and perhaps most important, it documents how the investigators were all reluctantly converted to a belief in the genuineness of Eusapia's phenomena….Since the earliest days of the British SPR [Society for Psychical Research], many of its influential members had been reluctant to deal seriously with the physical phenomena of spiritualism….Eventually, the SPR felt pressured to respond, and so they assembled a team of their most experienced, highly skilled, and skeptical investigators to study Eusapia one more time, apparently with the aim of justifying the Society's negative assessment of the medium. Indeed, it seems that the SPR officers and investigators all expected to find nothing but fraud when they tested Eusapia. The members of this team were the Hon. Edward Fielding, Hereward Carrington, and W.W. Baggally. Fielding had already detected numerous fraudulent mediums and claimed to be a complete skeptic. Carrington was an amateur magician who had recently published a book, three-fourths of which was devoted to the analysis of fraudulent mediumship. And Baggally was a skilled conjuror who 'claimed to have investigated almost every medium in Britain since Home without finding one who was genuine.'…Despite the rigid controls and good light, many impressive phenomena occurred during the eleven séances. In fact, the table levitated completely so many times that the experimenters eventually tired of that effect and asked Eusapia to produce something else. Moreover, many impressive things happened even while experimenters virtually draped themselves all over Eusapia….After the séances had ended, Baggally itemized and counted all the phenomena reported. He concluded, 'Eusapia was not detected in fraud in any one of the 470 phenomena that took place at the eleven séances.'…Far more riveting, however, are the reflections of the investigators written after each session with Eusapia. They document, with great candor, the intellectual struggle each investigator experienced as he reluctantly came to believe that Eusapia's phenomena were genuine. Skeptical accusations of favorable experimenter bias in this case would be outrageous." (Stephen Braude, The Gold Leaf Lady [Chicago, Illinois: The University of Chicago Press, 2007], pp. 47-49, 51)
Braude goes into much more detail in the book, if anybody is interested. I've left out a lot. See, also, Michael Sudduth's summary of the Leonora Piper case in his PowerPoint presentation under section IV here.
In another context:
"In response to one critic's assertion these scientists [who have researched near-death experiences] are biased and that near-death research has been influenced by the researchers' beliefs, [Bruce] Greyson [one of the leading near-death researchers] retorted that 'he has it backwards: the researchers' beliefs have been influenced by their consistent research findings. Most near-death researchers did not go into their investigations with a belief in mind-body separation, but came to that hypothesis based on what their research found.' In fact, one researcher, Michael Sabom [who later affirmed the veridicality of near-death experiences], entered the field of NDE [near-death experience] research specifically to debunk reports of the NDE." (Chris Carter, Science And The Near-Death Experience [Rochester, Vermont: Inner Traditions, 2010], p. 200)