Do you know how this was done? (Ghost in the mirror)?

Unfortunately, video and photos can't be authenticated. Especially now that there's video editing software that's affordable to almost everyone. I have software that allows superimposing two images, and even fading the one of the images to look transparent. I did see something on TV where a video expert was able to verify that a ghost video wasn't tampered with (splicing images produces a unique signature on the video), but there's no way to know if the guy was even a real video expert.