A "modernist" view of "reincarnation" or rebirth is that mind is a process (which is easy enough to confirm by sitting quietly and watching it process thoughts and sensations and so on) that functions independently of the brain, but which inhabits (one might even say parasitizes -- although it is a symbiosis more than a parasitic situation) a sentient being and when that being dies goes and finds another.

One could, as many Hindus and Buddhists do, assert that this is true because they have faith it is true -- on perhaps better evidence than Christians have for their Christ (incidents of deja vu and recalled previous lives), but to me it is not convincing evidence, not reproducible in any sort of scientific sense, so it remains to me an intriguing and maybe even probable afterlife, but not an item of belief.