How could either the occurrence of reincarnation or the existence of an afterlife be investigated scientifically? Both seem to presuppose something unknowable, such as a soul or an alternate spiritual dimension? There does not seem to be anything empirical that we can observe to confirm or deny such claims.
I can think of a way to research both. I’m not sure how rigorous either is. here’s how:
Afterlife. Choose a subject whose manner, place and time of death is known to only a few people. For example, a murder victim, someone who died accidentally, someone who commited suicide, of whom the details of their deaths are known only to the police, the ME, and the killer (if any).
Next summon the subject from the afterlife, assuming this is possible, using all safeguards against fraud (ask james Randi, or any half-competent stage magician for details). question the subject regarding the details fo his death. Do not offer him choices, merely ask him to describe when, where and how he died.
Finally compare such details to those you obtain from the authorities. If they match reasonably well, you may just have proved something.
Reincarnation. This is a bit different. For once you need at least two subjects for each experiment: 1) the dead person and 2) the person he reincarnated into. So you pick subjects whose life is documented but the details of which are very obscure. I suppose you’d start with people from the second group, then try to match them with whom they claim to have been.
The rest is pretty much the same. You queston the reincarnee and see whether the details match reasonably well.
Now, if you want to see whether a dead man can choose whom to reincarnate into, you could set up an experiment using volunteers before they die. Have them write down something, or tell them something, then see if, years alter, the reincarnee remembers those bits of information well enough.
Of course, this assumes there is an observed phenomenon that warrants further investigation. I do not think there is.