Probably T <= 0, multiple universes, inside a black hole, etc. You also can't run an experiment on your own life, not really, since you only have one life and that's not a large enough sample. So questions like "what is true for you, uniquely?"

Your life is definitely a large enough sample for experiments about you, since it covers the whole domain. No need to even use statistics.

You can know scientific truths about parts of your life, but you can't know scientific truths about the whole of it.

> Which phenomena would you consider not ultimately analysable via scientific methodology?

The physical existence of an external world, beyond my (TuringTest's) self-consciousness.